I haven't had this problem, but I heard of it once before, and helped the lady solve the problem.

This 7th generation of accord has a new feature that I love madly, which is the remote key-fob window down feature. The problem is, if your keyless radio receiver malfunctions and is easily fooled (rare) it can randomly active the windows roll-down feature for just a second, causing all the windows to be down just a bit when left unattended.

Even though this is unlikely, b/c you have said only the rear windows are slightly down, I thought I'd bring this up just in case. The lady I talked to before on epinions.com had all the windows rolling down just a bit. The fix was to have the dealer replace the keyless receiver thingy (for lack of better thing to call it).

It's a long shot, but it's an idea of where to start.

PS--as another LX sedan owner, I feel compelled to add this . . . The LX is no CHEAPER than any other accord. They are assembled on the same lines by the same people. The EX's (and V6's, etc.) are assembled under the same circumstances, they just have more accessories and doo-dads to mount. If anything, the Ex's (+) have a higher likelihood of glitches just because they have more sophisticated equipment to foul up.

To be honest, I'd love to have bought an EX (-L or such) with the nav and so on, but it didn't fit me, and I know that my car is of the same reputable Honda quality as the rest of the Accords. (Admittedly, even the DX's)