Ok, g'day ppl, I'm an electronics design engineer and I can't leave stuff alone - always pulled my toys apart as a kid.... but I got them to work again when I put them back together, sometimes added a few "modifications" of my own too, hehe
Anyway, I have been through this problem, 2 things -
1. You can get a new cradle from HP and it will work but it will still possibly have the problem until they change the mechanical design of the electronics in the cradle. It seems there is a problem with heat transfer causing poor connections during use (have you actually measured how hot the iPaq gets during charging ????)
2. HP will say I am wrong even though I had 5 cradles with the same problem, I "salvaged" 4 from ppl who ditched 'em when they got thier new one from HP

) and I have fixed my own personal one and now have no problems no matter how long I leave the unit in the cradle.
There is a problem with "dry joints" occuring due to heat transfer into the surface mount componentry on the small pcb within the cradle.
I have resoldered the suspect soldering and I have not had a problem since with my own, I have done the same for the other 4 ppl and they now have working cradles, I will be reworking thier other cradles one day too.
WARNING: The electronics in the cradle are based on fine pitch surface mount technology - if you do not already work with or do not have the proper tools to work on such hardware DO NOT ATTEMPT TO PERFORM THE REWORK.