Unlike the lack of 64-bit drivers, this seems to be a problem in Logic itself.  There's not really anything the Frontier Design folks can do about it.  Instead of deleting the Alphatrack controller and restarting Logic, try my trick of simply reselecting the Alphatrack MIDI port for input on the same screen where you delete the controller.  It starts working immediately and will save you a bit of hassle.

I think it might only like a non-latching switch.  I have a dual-mode switch and had the same symptoms when I first tried to use it for a punch-in.  I changed modes and it worked perfectly.  I'm also using Logic 9.

EDIT:  I wasn't clear on the modes.  It isn't a latching/non-latching switch but a momentary contact that can switch between normally open and normally closed.  In normally closed mode, however, it would look to the Alphatrack just like a latching switch that had been activated.  I still think that it really only wants a non-latching switch and it needs to be NO.

I just got my Alphatrack yesterday and the same thing happened to me.  It worked fine when I installed it, but when I turned on my Edirol keyboard Logic complained that the 'Alphatrack' MIDI port was missing and the Alphatrack seemed to be frozen.

I tracked it down to what appears to be a Logic 9 bug.  It seems that instead of using the interface name as configured in the Audio/MIDI tool it seems to be enumerating active interfaces at the time you configure a control surface.  If you start a new MIDI interface that moves the Alphatrack position in the list, it will stop finding it and disable input for the Alphatrack as a control surface and will instead treat data from the unit as a regular MIDI stream.

I went to Preferences->Control Surfaces->Setup, selected the Alphatrack icon, and in the inspector on the top left reselected the 'Alphatrack' port for input.  At that point, it started working normally again and the keyboard was not affected.  I haven't turned the keyboard off since discovering this, but I suspect I'll have to perform this step every time the number of active MIDI interfaces changes between or during Logic sessions.

Again, the Alphatrack unit isn't sending anything different in it's data stream (verified by using a midi monitor program).  I'm sure this is a Logic 9 bug.  It also seems to be confined to Logic, as I installed the Garageband plug-in and it did not have this problem.