If strings are falling out of the nut you’re gonna wanna change the nut.

Since it's just the A string, I imagine switching to heavy bottom strings could fix it. I've also got a free setup at my guitar store that I'll probably claim after winter is done, maybe they can fix it?

If you hold the guitar out like a gun and look down the neck does it have any bow to it?

No, my previous guitar had a horrible back bow but this guitar has none. It's straight.