I did notice when I owned my Cyclamatic, that the battery takes an awful beating from road shocks.
The whole battery actually moves up and down slightly in its mounting. This causes the poor contact with the prongs problem. Arcing from the movement, causes tarnishing of the contacts.
Also, the battery pack within the case, slides up and down inside the casing, thus compounding shock to the battery pack even further.
On the occasions that the battery did let me down, it turned out to be one of three things:
1) The prong contact thing mentioned in my other post. Bungee it down or find a way to secure the whole battery better.
2) One or more of the battery BMS leads had become disconnected, probably resulting in the battery being poorly charged. The plastic lid part which houses the charge remaining indicator needs to be taken off, and the battery pack slid out to check for any breakages in the wiring.
3) The positive wire attached to the key switch, had a habit of overheating and melting the solder, detaching the wire. It can cause an intermittent power problem like you mention.
It is a good idea, once you get the battery sorted, to pack out the top of the battery case with something to prevent the pack from sliding up and down within the case.
I removed the plastic lid on mine, packed it out with some foam padding, then screwed the lid back on.