Believe it or not, I also just got the AGM M14! May 1st actually. But anyways, at first I thought that I also had the same problem; however, it was just that I didn't push the mag in the right way. I doubt that you could be doing that everytime, but you might want to check what type of M14 mag you got because I've noticed that there are mags made specifically for G&G and CA (Classic Army) M14 models. Here's a link to where I found this out on Evike:http://www.airsoftpost.com/standard-magazine-series-p-28830.html
Hopes this might clear something up.
And I'm just curious if you could help me out also. (Trying to ask around before I make a new thread) Just last night, on the May 3rd, I was sighting in the scope I got with it and then my gun just stopped shooting. I'm not sure if it's the battery or not seeing as I discharged it when I first got it by shooting at targets until it gave out, but I did however charge it for about 4 hours (1100 mAh battery/300 mAh charger equals about 4 hours right?) but then when it gave out this last time, I charged it for an additional 4 hours yet, my gun still wont shoot. Also I've noticed that when I puul the trigger, it doesn't sound any different if the battery is plugged in or not. Could this be a connecter problem somewhere inside of the stock maybe? Ok... End of my rambling, sorry!