What is this box you call a linksys "extender".
The most likely problem is a bad cable. This is even more likely if the lights are going out and the port actually is going disconnected. It would be nice if a bad cable just stopped working so you knew it. What happens many times is one of the wires inside the plug is slightly loose and can make intermittent contact maybe be of something like very small changes in temperature. You could also be using a fake cable which makes these problems even more likely.
I would try a new cable. You need nothing fancy. Cat5e or better if it is cheaper. It needs to be pure copper (no CCA) and must have wire size 22-24 (none of that flat or thin cable). If you can't find this information on the cable look for another vendor, sellers of quality cable make it a point to show the specifications.