Lazyweb: please fix my broken eyeballs

For at least the last five years or so, I've been afflicted with this horribly annoying condition: if I don't get an average of about seven hours of sleep per night, then sometime around mid-afternoon my eyes begin to sting as if I'm having some kind of allergic reaction, and they'll continue doing this until I sleep.

If I have several nights of bad sleep, my eyes will begin to itch earlier and earlier in the day. The only way to make it stop happening is to get enough sleep to make up for whatever sleep debt I've incurred; then the itchiness goes away and my eyes are fine. In other words, two nights of bad sleep requires two nights of good sleep in order for my eyes to get better. On the other hand, if I get consistently good sleep for several weeks, then I can get bad sleep for a few nights in a row before my eyes begin to itch. It's as if I'm storing up sleep, and when I run out, my eyes punish me for it until I repay them.

The most frustrating thing about this is that even if my lack of sleep isn't enough to actually make me sleepy, it's often enough to make my eyes hurt so much that I have no choice but to try to get more sleep (which isn't always possible if I'm, say, at work).

I've tried everything I can think of to relieve the symptoms, including eyedrops and mid-day naps, and the only thing that works is for me to repay whatever sleep debt I've incurred, which often means I can't get any relief until the weekend (and sometimes not even then if I happen to sleep badly).

Does anyone else suffer from something similar? If so, how do you deal with it, short of just sleeping a lot?