FS8205A won't kick in
Lithium protection modules are usually designed to be permanently wired into a battery pack. When you remove one cell the protection circuit thinks the cell has become over-discharged, so it disconnects the output and waits for a charging voltage to be applied to the pack. Putting a charged cell back into the pack won't make the protection circuit 'wake up' because it thinks the cell is just recovering some voltage after being disconnected from the load. 

To make the protection circuit wake up you have to apply an external voltage, or (as you did 'accidentally') force the battery voltage to appear on the output terminal.