If it was a poor quality programmer, e.g. the proper programming voltages were too low, or not enough time was used, to properly program in the bits. I suppose, the programmer casually (relatively slowly) reading/verifying back the bits, might see the correct values.
But a relatively high speed processor (slow, by today's processors), needing rapid from the EPROMS (slow by today's standards, probably) data accesses, might be responding too slowly, because the programming has been done too faintly.
N.B. Above is speculation, there are other possibilities.
Have you covered the EPROM windows ?
Sometimes they can be sensitive to visible light, and stop working properly, without opaque labels on them. Ideal labels, seem to have aluminium (?) strips inside them, for near perfect no light leakage.