What three gospel groups that performed on the first National Quartet Convention in 1957 have not been invited to perform on the main stage of the 2008 convention even though they are still active full time groups in gospel music?

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The Chuckwagon Gang is one of them.

Besides Chuckwagon Gang, I'd say Melody Boys and Harvesters.

Blackwood Brothers are also not in this year's lineup but I'm not sure if you were including them since there are 3 versions of the group.

Well, What about The Blackwood Brothers, I have read that they are now a full time group again and I know for sure that The Blackwood Brothers were on the first convention. As for the others already mentioned the groups are pretty much only the same in name and I would not know if any of them have an a member that was with them in 1957 unless it would be Mr. Williams with the Melody Boys.
Also there is The Weatherford Qt. to consider.

Yes, you folks have come up with all the right answers. Even brought up a couple I'd missed. Actually, the Weatherfords weren't on the first convention, but have been on many since then.

Also, the Florida Boys aren't mentioned. I'm not sure if they currently fit the parameters of the NQC power structure, but they should also be considered.

Also, I don't think the Palmetto State Qt is on the program and these decisions were made before their implosion. No doubt they'll also be a viable group by the time September rolls around.