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I requested an invite there though I know it usually takes a longer time to get from the main source, so I didn't really count on that. It was one Twitter message that is floating somewhere on this virtual world that guided me to another source, and the next day within less than 24 hours, my invite arrived.
The person who sent me the invite is Giuseppe from Plazes, another web2.0 locator service that I already joined. Plazes developed integration with Fire Eagle that's way Plazes have some Fire Eagle invites to share -I think. The system integration between Plazes and Fire Eagle is done only with one click.
To learn about what Fire Eagle is, go here and here (this has some invites links, don't know if any of them still works)
To integrate it with Twitter, go here.
If you are still confused, ask me not :-P
Happy hunting your invite!