Same problem here! I've already described it in another thread:
I got a used 1.1.1 iPhone with 3.9BL jailbroken and unlocked about two weeks ago. Problem is that when waking it up from a sleepmode longer that ~15mins, the "Slide to Unlock"- slider won't react at first. Only after 15-45secs it reacts, unlocks and from then on the touchscreen reacts without problems- no dead strips etc. either. The problem only appears after a longer period in sleepmode when trying to use the "unlock"- or "accept call"- sliders (no problems with the other sliders- only sliders after sleepmode).
I've also tried restoring it to 1.1.4 and jailbreaking/unlocking it again- but the problem still appears without changes.
One fellow
in another forum (German) has apparently solved the problem by replacing the sliders with the "Tap To Unlock"-function. I've tried that, too- but no changes.
Any help would really be appreciated- a method to prevent the phone from really locking (just turning off the screen as dsedov mentioned) would be fine, too! Any ideas?