Trouble in Paradise - Significant drop when low battery or steep hills "pops" the switch and then won't turn back on

Hope someone can give me suggestion on what parts to replace to keep this scenario from happening. At this point I’d like to upgrade the parts, but I’m also willing to modify case and even configuration to create a more reliable set-up. I’m running a 10s Lipo battery.

Symptoms - Intermittent failure to turn on… With a fully charged battery, I push the on button, and it will either do one of three things - a) it turns on, and shows a full charge of about 42v., b) turns on, but only briefly shows a readout of say 30v or 32v, then immediately turn off, or c) not display anything on the LED as I press the button.

Eventually, and possibly days later, I can get it to turn on. But, after a session of 20 or 30 minutes, “goosing” or a moderate uphill demand, triggers shutdown (glad the system is working properly to save my battery, right…), BUT - then the system won’t turn on again, even though there’s still say 36v remaining in power.

One last piece of the mystery - When it won’t turn on, I can plug in the charger, and press the on switch, and it will turn on and hold at the 42V reading. When I unplug the charger, the read out turns off.

I’ve checked for loose connections and frayed wires. All is in good order. Would some kind sole tell me what to do to eliminate this frustration?

Hope my photos upload properly.