Here is a thread with an outline of the Ford TPMS system:
New Rangers TPMS System
The TPMS system isn't active until you reach 20mph and only checks pressure every 60seconds so delays are part of the system parameters.
If you have actually tested the pressure in each tire, and still get a light now and then, I would suspect a sensor in a tire is going bad, they do run off a small battery which at some point is too weak to transmit reliably.
I believe a $50 "reset" tool is needed to recalibrate the system, and that may not fix the problem.
Ford part number 8C2Z-1A203-A
The '08 F-150's came with the reset tool, manual even lists it as included in the reset proceedure