After shooting probably more than 20 rounds, the upper handguard to my Mosin slides forward. The rings seem to be tight, but the rear one clears the metal tab fairly easy. Any easy fix for this? Would some glue where the rings go work?

Bend the tab back to where it's supposed to be.

The Flat spring is fairly brittle so be careful bending it.

I would suggest tapping it out with a punch ( note hole on opposite side of stock ) and putting a cut piece of a rubber band in the slot under it to force it out and increase tension.

Another option is to file the the end of flat spring so it can catch ( more of a lip ) more of the rear band which tend to have very round edges.

Just fix the band retainer. Sounds like it is either out of form or off location. You can bend it out for more tention, but I would recomend removeing it from the stock first by use of a small punch and drifting it out from the thur hole on the opisitside of the stock. Other wise you risk snapping off the pin that holds it in the stock, and then you will need a replacement. It may also just be the cutout is recessed too deep. The forward section of the retainer should fall just below the surface of the stock. If it looks like it is way back in there you can remove it and shim it out. But only shim near the pin, or the sping will not have any where to compress to. Or the lazy option, it you dont take it apart vary offten or dont shoot it much would be to push the band in place the lightly drift the retainer out enough it will catch the band. It will work for a while before it needs redone, but the shock from fireing and the tension will eventually work it back in the stock.

Be very careful if you decide to bend it. They are very brittle and break easy.

The rubber band thing is what I would do. Put it close to the pin that goes thru the stock.

Or glue in a small piece of wood from a toothpick or popsickle stick.

Try not to do any filing if it can be helped another way, it's a permanent mod that can't be undone.