How will unmatched lithium-ion cells in parallel react?
Batteries in parallel will "charge" each other until they are the same voltage. You could think of it as each cell being a bucket of water. If you put a pipe connecting all the buckets from the bottom, (analogous to batteries in parallel) all the buckets will equalize to the same level of water. This wont harm anything if your batteries are all close to the same amp rating (+/- 200ma or so) I suppose if one of your cells is bad and "leaking" energy the that could be causing your issue by constantly discharging all the other cells in your parallel bank...

All in all, batteries in parallel balance themselves automatically. Where you need things to be actively balanced is with cells in series or packs of parallel batteries in series with other packs. That active balancing is done with a balancing charger or a circuit in the pack. As long as all the packs connected in series are the same summed capacity.

Hope that helps!