I had an frustrating experience with a drawn game recently. After we had exchanged off our Rooks I, as Black, offered a draw with this position:
My opponent played on (no acknowledgement of the draw offer), which was OK with me, but I couldn't see how he thought he might get anywhere. Still, he ran around, and tried this and that, all of which was easily countered, and after waiting patiently for 21 more moves (and 8 days) during which the prospects for a draw didn't change, I again offered a draw. Again there was no acknowledgement and he played on.
Now I was irritated, so I turned off the chat and began offering a draw after every single move I made, thinking he might at last get the idea. No dice. I finally was able to force 3-fold repetition on move 65.
Just for a lark, I had Rybka take a look at the final position and the position 32 moves earlier when I had first offered a draw. Rybka's evaluation of the final position was 0.00, and it's evaluation of the earlier position was +0.04.
When I am sort of losing, I do not blame them for declining my draw offer. When it is clearly a draw, however, it can be irritating, especially if it is correspondence chess and the other player is slow to move.
There is some gratification though when I win after I have offered a draw and they have declined. :-)