In general, if there is an intermittent problem that comes and goes when you bend a particular cable, it is due to either a break somewhere along the cable, a break in the cable at or near the point where the cable enters the strain relief on the plug (and I use that term loosely; often the so-called strain relief on cheap cables is too rigid to relieve any strain and just creates a weak point where the wire emerges from it), within the plug (less common), between the plug and the socket (uncommon) or between the socket and the circuit board (this can happen if the item is dropped and lands on the plug; the circuit board can be broken and/or the solder joint(s) on the plug can break.
That should all be fairly obvious, as is my suggestion to gently wiggle the wire and plug in various places to locate the break as accurately as possible.
From your description it seems that the power is OK because the second channel of the amplifier (that drives the daisy-chained speaker) always works; it's only the channel that drives the first speaker that is having problems. The connection from the amplifier to the speaker is inside that enclosure and unlikely to be the problem.
My guess would be that there's an intermittent break in one channel in the wire that runs from the main speaker to the signal source. I assume this ends in a 3.5 mm stereo plug that can plug into a laptop, iPod, etc. As I said, the break is likely to be right where the wire leaves a strain relief, either at the speaker end or at the plug, and you can locate the break with gentle wiggling.