Hi,
Firstly, a word of warning, there are fake Teensy boards from China origin around which simply do not work in context of the GliGli upgrade. They are offered on ebay for cheap but they are of no use for us. I discovered this when a friend of mine asked me for help. It was the board! He ordered two and both didn't work. Just use the original ones.
The described problem could be unfortunately anything: voltage regulator issue, dry capacitors in the rectifier stage, lose wiring, EPROM connectivity issue (socket / pins corroded) , defective logic ICs, etc. etc. Yes, looks as if the CPU sometimes doesn't reset properly but the issue might be somewhere else. Always a good idea to check the different supply voltages FIRST. Hard to judge from the remote.
An experienced techi should be able to find the issue(s) with some systematic measurements.
Good luck.
- Pete66