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. :-)

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. 

I would definitely have accepted Cystem's draw offer, now, but, not too long ago, I would have played on as White, simply because I had to learn from experience that there was no way to win. I also didn't know that declining a draw required a response, other than just playing on?

Sure, no response is required, but I've had a couple people type in something like "not just yet" or "I think my position is good" .  A response isn't something I'd expect.

Also, the fellow I was playing was no noob-- he had almost 650 CC games played, with a rating just below 1700.

Oh.

I've had this happen to me many times on this site.  And the guys who decline (often) suddenly start playing the endgame a LOT better than they played the game up to that point.  I have at times found that to be suspicious.  They play the game like a 1400 up until you offer a draw, and then suddenly they are Bobby Fischer in the endgame.  Most of us lower rated players aren't great at the endgame, so when a guy performs WAY better in a complicated endgame I have to wonder.  

But thats ok.  There is always the next game.  

I just had a sweet one where I offered a draw in a position where all I had to do was not lose my mind and let my opponent into my position and I could hold forever. Of course, he turned me down. A few moves later he dropped a piece and resigned.