Since you are the original owner, I assume that there have been no weirdo electrical repairs or modifications made to the car?
Does the radio only cut out when you flick the high beams for passing or does it also cut out if you switch the high beams on permanently (there are two sort of separate circuits)? Also, when the radio switches off, it is completely switching off or just the lighting that is switching off, or just the audio?
My take is that all of the NSX radios are the same over the production run; but, I don't know that for sure. I have a pin out for the 1991; but, the service manual / wiring diagram for my 2000 is in the trunk of the car which is now in storage so I can't compare the pin outs. I am pretty sure the plug is the same; but, if you can, check the pin out for the 1995 radio to make sure that the wiring arrangement did not change. I don't think that is the problem; but, best to eliminate it as a possibility.
Both the radio and the high beam lighting control are tied into the security control unit. I think; but, am not sure, because the service manual does not provide details, that the security control unit gives a +12v signal to the radio when everything is good. If the radio loses that signal, then it shuts off. Your operation of the high beam may be causing the security unit to do something to the signal to the radio. (Edit - On further checking, I am a little uncertain about this last bit. The service manual says that the wire between the head unit and the SCC is supposed to test out at ground potential. So, I am not clear as to whether the connection causes the SCC to go into alarm when the radio is disconnected or whether the radio needs a permissive from the SCC to operate. Unfortunately, the test procedure has no discussion of the SCC / Head Unit interaction and doesn't list the head unit as one of the alarm triggers.)
In the absence of some more definitive symptoms, I am really doing a lot of guessing! With some more details, I may be able to suggest some simple tests. I don't think that it is a capacitor issue if the head unit operates normally when you are not busy flicking your high beams!