I've probably written this several times over the years, but like a car that requires Fuel, Air and Spark, provide those and it's guaranteed to work, a PIC also requires three things, and in the PIC's case it's Power, Clock and Reset. If you have those correct, the your PIC is also guaranteed to run.

From what you write (which is very little and doesn't give us much information on which to base a comment), I'll suspect a power supply with a very slow rise-time at Power-On. If it's a Battery, it's probably weak. If it's from a dedicated Line Power Supply, is it under-rated for the current you are drawing from it? If it's a weak PSU and if you have large smoothing Capacitors then that could also be a reason.

Melanie