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Is that the same 4.0.2 that is shown here: https://sites.google.com/site/diygeigercounter/technical/archives?authuser=0 , under the 'GK-B5 Schematics - older versions' heading?

That would certainly do it, I think. The ATMEGA328P micro-controllers can operate down to about 1.8v but the 5v supply (from the regulator) also powers the other electronics for the HV PSU and the ring oscillator (74ACT14N). The minimum voltage for the 74ACT14N is 4.5v and as it is that IC that sends the signal to the micro-controller it very well may be that causing the erroneous counts.

If it helps I have version 5.5 on a breadboard. It is only the PSU and detector circuit and I feed that into an Arduino Pro Mini.

Let us know how you get on after changing the regulator.