He has the right to offer a draw, you also have the right to refuse it and kick his sorry little hiney into the 1-0 corner.
Appropriate Draw offer?

What is the rating of each player? What is the time control? How much time left on each clock at the time of the draw offer? Were previous games acrimonious or friendly?
This ticket is now in NeedsMoreInfo state.

White was higher rated than black. Both are rated high enough to see what's coming. White's last several moves have been purposefully opening the h-file with sacrifices. White has 2+ minutes to calculate a very straighforward win. There were no previous games.

I had an opponent here offer me a draw in s similar situation, he was completely lost and it was turn based and he was over 2300 in turn based. I answered by asking him did he really think the position was drawn and he answered and said no. So, I then asked him , so why offer a draw then if you know you are losing ? He didnt answer but he did resign. It takes all kinds I guess...

well,one perhaps could understand a first offer,I guess he had to try it. But the second one was just too much IMO.

Yeah, I could see a draw offer in a position like that being a little rude, but even more so it would simply be hilarious.
I admit, i have thought of offering draws in clearly lost positions. But it has always been with games against my dad, but i am pretty sure he would accept rather than just laughing and letting me resign or be mated. Although, he did offer me a draw when he was (knowingly) one move from mate, but that is a longer story. He actually shortened the mate by one move to offer the draw again.

I think its an internet thing, if it was over-the-board you wouldn't even consider offering a draw, at that level you would just resign. The draw offer in this position is obviously very rude, but unfortunately thats what happens online.

And Loomis, you don't have the right to offer a draw at anytime, and your opponent clearly violated the laws of chess. I know that this rule is hard if not impossible to enforce here, but the Fide laws of chess clearly say:
Article 9: The drawn game
9.1
b. |
If the rules of a competition allow a draw agreement the following apply:
Article 12: The conduct of the players |
12.6 It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.

And Loomis, you don't have the right to offer a draw at anytime
I wasn't precise enough in my language. I should have said, a player has the right to offer a draw on any move (at the right time). Meaning simply that the rules do not explicitly prohibit offering a draw in a lost position.
In the example, the player made the offer at the right time according to the rules -- at the same time he made his move. The question isn't about whether the rules prohibit the draw offer, but rather whether the behavior is simply rude (obnoxious, annoying, childish, poor etiquette, etc.).

He has the right to offer a draw, you also have the right to refuse it and kick his sorry little hiney into the 1-0 corner.
There's no question that he has the right to offer the draw. I stated as much in my original post. The question is whether the offering of the draw is rude (obnoxious, annoying, childish, poor etiquette, etc.).

And Loomis, you don't have the right to offer a draw at anytime
I wasn't precise enough in my language. I should have said, a player has the right to offer a draw on any move (at the right time). Meaning simply that the rules do not explicitly prohibit offering a draw in a lost position.
In the example, the player made the offer at the right time according to the rules -- at the same time he made his move. The question isn't about whether the rules prohibit the draw offer, but rather whether the behavior is simply rude (obnoxious, annoying, childish, poor etiquette, etc.).
I would have classified that behaviour exactly as you did.
And, if his first offer could be somehow justified by some(and I don't say it can), his second one doesn't have anything to do with the draw offer, it has everything to do with annoying an opponent, which is clearly forbidden according the 12.6.

I have offered a draw, simply as a joke, while I was clearly losing. Although it was usually against someone I either knew personally, or played often. It is clear however, from the OP's opponent's responses that the intent was not humor.

I dont think that offering draw at anytime is considered a rude behavior. For the following reasons:-
(1)-The player is using his right given to him by the FIDE. & his oponent has the same right. the same way I can not consider resigning in a wining position is a rude behaviour, simply because the player has the right to resign even if he thinks he is winning. Using ur right can never be considered a rude behavior. otherwise we should not name it a right.
Right = ie u r not disturbing anybody by using it.Otherwise it is not right.
(2)-The player who offers draw in a losing position may be expecting a mistake from his opeonent & this is agian his right to do so. Yes it is not happeing so frequent but also not rare an openent may commit mistake at the last moment. So he has the right to expect mistakes (like not seeing the mate moves, blunders, stalmate.etc).
(3)-Chess is similar to a court, where no body can be forced to accuse himself or resign or confess about his guilt. Because he is using his right to defend himself till the last moment in his life.& it will not be considered as a rude behaviour to defend himself.
(4)-Interpretetion of any position is a relative thing & depends upon how deep u understand chess. Somestimes we see a GM who resigns in a position in which we think he can continue & vice versa. so If Mr Loomis is playing with a GM, that means all his offers of draw will be counted as a rude behaviour!, because the position that Mr Loomis consider it as an equal, it may be seen from the side of the GM as a clearly lost position!. so he has no right to offers any draw. I think this just rediculous!.
(5)-Why Mr loomis is bothered by the draw offers of his oponent if he thinks he can win easily?! why not just win the game & ignore the draw offers?. I think the real reason behind the nervousness of Mr Loomis is the lack of self confidence & lack of knowledge & ofcourse not the draw offers of his oponent.

And Loomis, you don't have the right to offer a draw at anytime, and your opponent clearly violated the laws of chess. I know that this rule is hard if not impossible to enforce here, but the Fide laws of chess clearly say:
Article 9: The drawn game
9.1
b.
If the rules of a competition allow a draw agreement the following apply: A player wishing to offer a draw shall do so after having made a move on the chessboard and before stopping his clock and starting the opponent’s clock.That's quite a trick on chess.com!

I dont think that offering draw at anytime is considered a rude behavior. For the following reasons:-
I don't want to quote a long list, but I'll respond to your points by the numbers you gave them.
1) You claim that anything you have a right to do can not be considered rude. It is not possible to prescribe rules for the actions in your life that cover 100% of scenarios. The rules do not prohibit offering a draw, but that does not mean that general etiquette wouldn't consider the offer rude. There are many things that are not strictly against the law, but are still bad behavior.
2) If you expect a mistake from your opponent, let him play the mistake and then you win. Easy as that. Asking the player for a draw is like asking your opponent to not even try.
3) I don't see how the issue of not having to resign has anything to do with pleading for a draw in a lost position.
4) You may have some unique understanding of the example. I bet you would agree that both players knew full well what was about to happen and the one offering the draw was trying to escape from what they knew to be a lost position.
5) This question isn't about personal attacks. In fact, I did simply play the checkmate in the game. My question is whether or not it is rude to put someone in a position of having to decline their repeated draw offers in an obviously losing position.

In otb chess too many draw offers is not allowed. The arbiter can be called and the offending player can be punished if they persist in offering draws. Common sense should tell most people that its not good sportsmanship to offer a draw when you are losing and this is compounded if, after your opponent declines, you continue offering draws. I sometimes think it would be best if the draw offer worked like the doubling cube in backgammon..... if you offer a draw then the ability to offer a draw passes to the opponent and you are NOT allowed to make multiple draw offers.
My opponent has just played Rf8-e8 and then offered me a draw.
Of course, white has a forced mate on the board. After ... Rh1 f6 black offered a draw again.
I found these draw offers to be insulting. I asked my opponent after the game why he offered a draw. He said he should try everything to avoid the mate.
What do you think? Is it rude to offer a draw because you see you are faced with a forced checkmate? Or does the fact that you have the right to offer a draw at any time make it ok to offer draws in these kinds of positions?