Draw

What is the etiquette for making draw offers when you are clearly in a losing position? Also wondering for when people time out when they are losing. I presume the latter is so at least they make you waste minutes waiting for them to move, and they hope that you abandon the game?

@1
"What is the etiquette for making draw offers when you are clearly in a losing position?"
++ If you are clearly losing, then resign, do not offer a draw. The Laws of Chess forbid unreasonable draw offers:
"11.5 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."
https://handbook.fide.com/chapter/E012018 

"when people time out when they are losing"
++ They can use their time as they see fit. Maybe they are looking in vain for a way out.

Soemtimes losing players can take a long time to move, but some don't play for 7 minutes or more just to "get back" at you

In person (not on-line) I can understand offering a draw in a losing position if your opponent is in severe time pressure (in which case the clock may mean your position is not losing).  When similarly doing so on-line I guess you'd have to balance whether or not a draw offer interferes with what shows up on the opponent's screen.

That said, when people offer a draw in a losing position they might not realize that the position is losing (and they may be the ones correctly analyzing it).

Also, match or tournament considerations may come into play.  An opponent who can clinch a team match victory, or who can clinch clear first in a tournament, may accept a draw offer just to eliminate the chance of a later blunder giving it all up.  In non-rated tournaments I've offered draws from winning positions when it clinched first.

It is not a complain but simply a question from a beginner.... I wish to know what chess etiquette says about a following situation:

Endgame: I had two pawns and king, my opponent had one knight and and a king (and no pawns). Because my pawns were quite badly on the table I offred a draw (more than once) and my opponent rejected it.

Was it reasonable to reject a draw offer in that situation?

Thank you in advance

Draws don't have to acceped even in theoretically drawn positions. Depending on the time available on the clock and the regulations played under, your opponent may have been hoping for a win on time.

I was asking because I have seen that a situation when one side has timeout and other side has insufficent material for checkmate is a draw for chess.com.

The game in question ended with draw because same position repeated three times.

ok insufficient material is a weird topic

chess.com bases it on the material you have (so a knight isnt enough) but fide bases it on technical possibility of a mate with legal moves (so a knight can be enough, given positioning of the pawns)

and this also applies to normal insufficient material not just vs timeout

anywhere though, if the non timed out person had "sufficient material" they win and if not its a draw