I run into a slightly different problem when I listen to a composition over and over again, although this may be something that only happens to me: it gets too easy to get "stuck" thinking about the piece in a certain way. That is, I get used to hearing it follow a certain path, and then it gets hard to even imagine it doing something different and still making sense.It's a similar problem, but has to do with losing imagination rather than becoming "deaf" to flaws, I suppose.
As for the OP, I will repeat royreintjes' advice and say, try to write in larger "sections" instead of bars. You can work on separate sections independently as long as you check their transitions and their overall function in the piece to make sure everything's fitting together properly. Sometimes you can save yourself the time actually listening to a previous section if you can recreate it mentally--or, again like royreintejs said, the "feel" of it, if not the literal details of how it worked. Visual representations can be helpful for this--i.e., if you're writing on staff paper or in a MIDI sequencer, glance over the other sections and try to "hear" them in a rapid, summary sort of way without actually performing them or pushing play.
Another strategy, which I'm really bad at myself, is to plan out how you want the piece to go ahead of time. You might draw a little diagram, maybe something as simple as a line that rises and falls to express tension building and release, and then keep that in mind as you write--think about where you "are" in the piece, where you've come from, where you're ultimately trying to go. (This doesn't need to be set in stone, of course you'll probably revise the overall plan as you write.)