Does your board try to use the old style resistor/capacitor reset circuit? If so you should get rid of this and install a good quality reset generator chip. These hold the reset line at the active level till well after the VDD rises to a valid level. Then you can be assured that the initialization logic of all the SFRs onboard your microcontroller is done properly.

You should also look at all the chip specific SFRs and carefully consider what your software is doing to initialize them to the values that are compatible with your use of the chip. Often times the reset state of SFRs may not be proper to how you are expecting the chip to run.

Check also what is going on with the VDD and GND lines of the microcontroller during a power-on cycle using a good DSO (digitial storage oscilloscope). If there are dips, rises, pulses or glitches on the VDD or GND right near the end of Reset or anytime thereafter then the microcontroller will be unlikely to be able to run its code reliably. Its been said a 1000 times here on this forum....but....do you have sufficient decoupling capacitors on the VDD to GND connection of the microcontroller right near the pins?

Michael Karas