I'm not surprised to hear this... and I expect that, eventually, I'll see this on my own Archos devices as well.
It sure sounds like some of the solder joints affixing the lower-edge connectors to the main PCBA (printed circuit board assembly) have failed.
This is something I'd absolutely expect to see happen if, for example, someone used their device on a DVR station without the "saddle" for their particular unit. I'd also expect it if they used various plug-ins while traveling, etc, and "bumped" them, fairly hard, a few times. But even without any abuse of the sort mentioned above, this is likely going to happen eventually on some units.
The little lower-edge connectors are soldered onto the board, and are in no way secured by the case itself. They are held on to the board by solder joints. I do not believe that there is any other means of attachment to the board. (I've had my A5IMT and A5IT apart a grand total of one time, but I inspected it in great detail while apart.)
Overload those joints, or just "normally" load them frequently (and I'm talking about physical loads, not electrical ones, by the way) and the solder joints will likely fail.
When this fails, it will probably not be on every single "pin" of the connector, just one or two of them. At least at first.
I had a similar experience with my first cell phone, a Motorola StarTAC. It had a similar lower-edge connection and the phone would plug into a charging dock along that edge. Eventually the solder joints gave out... meaning I could no longer sync my phone to my computer, or charge my phone. I was able to charge batteries externally, so the phone remained useful. Eventually, I took the phone apart and resoldered the entire lower-edge connector (not adding solder, just using a hot iron on each little tab). This totally restored the device's functionality. I then put epoxy over the connector tabs on the board, and along the edges of the connector body... so that the stresses would be carried by the epoxy, not by the solder joints. While I no longer use this phone, I had it out a few months back (just "playing" with it... it's not registered to any carrier anymore) and the connections are still in perfect working order.
The Archos lower-edge connector is somewhat more robust than the one on the StarTAC was, but not by much. If you put a lot of mechanical load on that little connector, or just plug and unplug stuff very regularly, it's inevitable that some joints will fail, eventually. I expect this to happen to my own eventually, in fact.
But if you have a decent soldering iron (very fine tip) and steady hands, you can likely recover the full use of that connector. And if you're sure the joints are in good "permanent" condition, you may want to pot them over with epoxy, as I did to my old phone, to reduce future stress on those joints.
The pins, where the connector adjoins the printed circuit board, are VERY small.... and you can't allow any "solder bridges" between pins. So if you're not sure you're up to the task, you may want to find someone better equipped to do it for you.