I've had this same issue since I started using AirPods. I've purchased 4 pairs over the years & all of them seem to have the issue at different times, with different sides (sometimes it's the left, sometimes the right). I THINK I have finally figured it out. In my case, manually pushing the AirPods forward in the case usually solves the issue, but only as long as I put pressure on the AirPods. Once I let go, it will go back to not charging.
The solution I found, after lots of trial and error is to put sticky tack (that stuff they use in school to hang stuff on the walls, Gorilla Mounting Putty is the one that I use) in the top of the case & then cover it with a small piece of paper. I put it in the part of the top holes in the case that are closest to the hinge & then up into the peak of the hole, and then cover it with a small piece of paper. I just used a torn off corner of a receipt. It took a couple of tries to get the right amount in there, but when I close the case it took a slight amount of pressure to close it, but after that, the putty moulded to the shape of the AirPods & it closes fine now. And it's been 3 days & both AirPods in the set have charged every day so far.
If something comes up and this stops working, I'll report back, but so far, so good.