Currently testing on my 3ds. Posted another answer a few minutes ago saying that it didn't work on regular DS games, but I decided to test it and see and it works on a few.
Pearl/diamond: Soft resets
Hg/ss: Soft resets
W2: Soft resets
I have had this issue before, so I know exactly what you're talking about. Here's some things to try:
-Try pushing harder on your buttons, and at different speeds. Test to make sure all your buttons are working correctly in game
-Look at the L = A in the game settings. don't think this would impact the DS, but it could be making the game read the L as A if it's on.
-It's possible the game is faulty, or the DS itself. Is the game legit? This (might) have an impact on how the DS reacts to it. If you have any knowledge on electronics, it's possible that something regarding the 3DS's L and R buttons is off or broken, as a general manufacture error. If you have knowledge, taking it apart and seeing could be worthwhile, but I would not reccomend doing that if you don't have experience. It's better to get a refund and get a different one.
-If all else fails, you get a new DS, your game is legit, all your buttons are reacting properly, I'd reccomend trying to use an old fashioned regular dsi. They restart and reset quick with the power button.
Good luck on your troubleshooting and journey!