I also had a problem once that 8051-mask ROM device was running OK, but C501-OTP with burn-in the same program was not running at all in the same circuit.

I've found out that C501 had larger transient current spikes when running than 8051-ROM. (The average VCC current consumption of both processor was the same.)

The problem was that it was a commercial product - a small telephone system and therefore approved. And for that reason, there was a small ferrite choke in a VCC track to reduce EMI. Current spikes of C501 induced such high voltage in the choke that VCC voltage variations of 5V were high above 1V Vpp (measured with oscilloscope). So the supply voltage spikes were disturbing the processor not to run properly.

Maybe this could help you more.