Like everyone says, one you have the Non-A you are good for the dates specified, individual units cannot make local policy that conflicts with JFTR (unless there is some operational reason, ie security).

But you are new to unit and it sounds like they are trying to save coin. You might want to talk to some of your peers or more experienced guys...if this policy is some JO or NCO shoe clerk's idea, don't worry about it. But if it's something the Boss mandated or supports you might be muddying your own waters. I wouldn't move just yet, but ask around to get a feel for what's behind this.