On the loom side of the connector you'll see the brown earth in one corner with no wire next to it, the perm live and remote on are at the other end side by side. The remote on should be 12v+ with the HU on and drop to 0v when off. The perm live should be 12v all the time. Obviously you'll need to wait until the fault develops before testing. The connector is clipped to the sub enclosure so if you can unclip it then you may be able to get to the sub side of the wiring without removing the boot trim, but it'll be tricky working through the small cubbyhole opening. Ideally remove the boot trim so you can get proper access to the sub.
I suspect if it is a wiring problem (rather than the amp itself inside the enclosure) then it's most likely the remote on, as this is very low current, so any slight breakdown in the connections will mean it'll drop voltage very easily. The perm live is carrying all the current so can withstand a bit of resistance in the wiring. The remote on is just a trigger to the relay in the amp to turn it on/off with the HU.
Without taking the whole sub out, it's going to be difficult to establish if the dodgy connection is on the other side of the loom (the wiring going to the amp). This is also a weak link as the wires are soldered onto the circuit board inside the amp and it could be something as simple as a dry joint on this connection. Dry solder joints are very common as equipment gets older, and can be intermittant so difficult to find. In these situations I would run a soldering iron over the soldered joints on the pcb to ensure they are all OK, but you need to remove the sub in order to do this, which is quite a job as there's lots of trim to remove to get to it. If you need instructions on how to do this then PM me your email address and I'll send them over.