Rather than recounting all the gory details, just read this including the comments. It sounds like there are some major personality issued involved and maybe some policy issues.
The former AIP Vice Chair, J.R. Myers, has resigned from the AIP and is attempting to start an official Constitution Party affiliate in Alaska. While not technically an official CP state affiliate, the AIP has in recent years essentially served as such. They gave Michael Peroutka their ballot line in 2004 and Chuck Baldwin their ballot line in 2008. They participated in the 2008 CP National Convention as official credentialed delegates.
I do not have a detailed understanding of all the personality issues and internal intrigue involved here, but in a vacuum I do think that it would be better for the AIP to officially affiliate with the national CP than for a new Alaska CP to be formed. Not only does the AIP have a history compared to a new start-up party, but as a Southerner I like the fact that an openly secessionist party exists and is still active, and I would really like for such a party to be affiliated with the CP so as to keep the CP honest on the matter of secession.