wow, this is a first. I just booted up my Xbox and it says my profile is invalid and I have to recover my gtag. I had recovered it at my dad's where I was house sitting and I've come home to my crusty old shitbox and I get this.
I'm totally fine with this 30 minute process, as I should be doing homework anyway. Thanks MS for putting me on the right track.
Get a USB stick and keep your profile on it.
If you use "Recover," you are risking losing compatibility with your existing save data files. When you "recover" your Gamertag, the system has to know how to consider the new file valid and invalidates the old one. This ostensibly prevents multiple people from using the same GamerTag simultaneously, though in theory you could have someone maintain the original GamerTag and just play offline consistently.
Anyway, hope there weren't too many games with incomplete progress on your profile.