So, the bad news is that I just sent out the last 3 of the 5 invites I had.
The good news is.. when I logged in to do that, I noticed I had been given 2 new invites to replace the ones I'd already sent out. \o/
So, it looks like the beta invites might be an unlimited resource, but you can only add 5 people at a time. Will find out if I get 3 more back after the monkeys I invited accept tommorrow.
The other good news is that I used the invites for 3 of my friends from Doomcast. They should have their own set of invites to hand out in a short while, and I'd point you to this thread on the Doomcast forums if you're looking for one.