The supplicant is configured via GPO.
I actually tweaked the supplicant/server timeout settings on the switch and I think you were on to something. I changed the port's Supplicant Timeout/Server Timeout setting to 300 seconds and was able to say connected for 5 minutes. Which, of course, begs the question of why the same behavior isn't displayed with DomainMachine/DomainUser logins.
Thanks for the assistance!