Can anyone help me? I have a 2001 F150 with factory keyless entry, is there anyway to have the keyless entry work while the engine is running?

 

Unfortunately no - the TCSM software was implemented this way to prevent inadvertent activation of locks or PANIC while the vehicle is running (i.e. kids playing with fobs).

Some vehicle lines have already changed to allow operation with key ON, but F150 is at least a few months away yet.