This seems to have been an issue with early eDGes. My first one, purchased in early May, has this issue but recent ones pop out easily. I tried to use the shake method that Boris recommended to me once for my personal one but have gone to a slight modification of the battery (shaving the edge with my swiss army knife) as the ultimate solution for my Generation 1 eDGe (no X).

The springs are definitely stronger (actually exist). We have now worked with almost 75 eDGes since August 15th and have none that show this issue as we remove the battery as part of our set up process with learners and none have shown this issue. I could say that this is only a recent occurrence but about half of the eDGes we have used are coming with Badger installed.