The 1/8th mini-plug jack on the GL2 is a poor link in the audio chain. These types of connections are prone to failures because of the weak spring clips that are supposed to push against the mini-plug when inserted. With repeated use, the spring clips get weaker and weaker until the connection becomes intermittant or it fails completely. Another issue that adds to the problem is long mic cabling that creates side loading on the mini-plug jack and causes further weakening of the spring clips. The same thing is true for the headphone jack, or any 1/8th inch mini-plug jack for that matter.
If your camera is not under warranty then my suggestion is to take it in to a good repair facility and have them replace the min-plug mic jack. They may be able to simply bend the spring clips back so the connection is better, but usually replacing the components is the best fix.
To prevent this from happening again you need to have a min-plug cable custom made with a 90 degree plug at the camera end to eliminate side loading, with the appropriate adapter at the other end for your actual mic cable. It’s far cheaper to replace the mic cable from lots of use than it is to replace the GL2’s mini-plug jack. Buying Canon’s MA300 XLR adapter might be an option for you. This way you don’t need to use the mini-plug at all.
Or you can get one of these:
https://www.beachtek.com/dxa4p.html
– Don