So I got the .223 pistol (That Gun) found in the dino gift shop and had it for awhile, after retrieving the All American from vault 34, I noticed it had disappeared from my inventory. Anywhere I could find, steal, or buy another?

P.S. I am 100% positive that I did not drop the weapon, let it break, sell it, or place it in a holding area (crate, box, vending machine, cabinet etc.) This is so far my favorite unique and I'd love to know how to get another.

There's only one copy of That Gun in the game, sorry. There is, however, a generic version (5.56 Pistol) that you can get with GRA.

Ugh, damn, ok. Thanks for the help though. Il go check go runners

Maybe you gave it to a companion and entered a casino or similar place where you got stripped of your weapons. It's a bug that causes The companions to never get the weapons back after exit. You could use the console if you play on pc.

Nah, I'm on PlayStation so console commands aren't exactly gonna help