I wondered about this for a long time, having had the same experience (though not very frequently). One time I kept inquiring through the chatbox, "Are you still there?" etc. After a long pause, my opponent replied, in effect: "Sorry -- I'm at work and my boss walked by." I suspect that some live players have something come up that keeps them from both continuing play and from disconnecting.

I, of course, am shocked, shocked that people play chess while they're at work. I know I would never do such a thing. I mean, to me, that's just wrong.

(HAHAHAHAHAHAHA...)

ive never really played live chess for that reason. The first couple times i played that happened. Thats why i play turn based games. i only play live if its against a friend.

Yes, I have experienced this quite a bit, especially over at FICS. I don't play live chess here anymore because it just doesn't work well for me. It happens mostly when I play as white. One reason I thought they might be doing this is that if I play 1.d4 but they don't want to play a QP game. Or, they don't like the time setting or the color they drew and they didn't bother to look at the seek properly before accepting it. Sometimes it will happen 2 or 3 times in a row. It's frustrating. Just like you, all I want to do is play.  

turn based chess is better than live.