Disappearing draw offers

I just played a move in a game when I was directed to the game from another as my "next available". After making my move, I checked my email and saw that I had a draw offer in that same game. When I clicked on the link to go back to the game and consider the draw offer, there was no draw offer. In another game recently, I made a draw offer and got no reply as my opponent was off line for a couple days. It was my turn to move and I was looking at possibly losing by time out while my draw was pending. Would that have happened if I did not move? And did my draw offer disappear when I moved?

a) You must make a move regardless of the draw offer. If you offer a draw and do not move is your time that is counting down

b) If you opponent make a move and do not answer the draw offer it is automatically rejected (I believe).

If your opponent makes a draw offer and then you made your move in the game (which I think you are saying is the case here) and then realize that your opponent offered a draw then it is too late. The action of playing a move in the game is also a simultaneous action of declining/ignoring the draw offer.

Thanks for the replies.

Streetfighter, I didn't know that. Thanks for the info. I will move first and then offer in the future. I have a game in which I may offer now. A careless couple moves yesterday kept me from trying my hand at a rook v. bishop endgame. It will be a king v. king endgame soon.

I'll try to do that after the game ends, which should be tonight or tomorrow. I've never posted a game/position before. It is rook and pawn v. rook and bishop. Was rook and a couple pawns v. bishop and a couple pawns. I was thinking I could not win rook v. bishop and he could not win with just a bishop so I always had the option of sacrificing my rook for his bishop and forcing a draw that way. Then I saw an article on Chess.Com showing how rook v. bishop endings are often won when the players are rated below 2000 and started wondering if I blew a chance.