2W900FM remote temporarily stops working

I just installed a 2W900FM-AS over the weekend.  Everything is working pretty well except that after I get out of my car and it arms, the 2 way remote stops working for a while.  I haven't tested how long, but it's probably at least 30 minutes.  Here's what happens:

I stop the car and do the reservation mode sequence* (this is my normal shutdown routine so I do it everytime).  I take the keys out (engine still running), get out and close the door.  Engine shuts off and the alarm arms just like it's supposed to.  The problem is that now my remote won't communicate with the brain.  If I query immediately after it arms, it shows no signal on the display.  Same goes for all the buttons.  Eventually it'll start working again, but I'm not going to carry two remotes around for one car (the 1 way is working fine).  Any ideas what might be up with my remote?  I can't get it to reprogram during this time either.  Also, the display will sort of freeze at the last status of the car (it'll show it locked and armed, but of course none of the buttons work).

*I haven't tried arming the vehicle yet without going into reservation mode.  Maybe this has something to do with it?

Thanks for the info.  The last time I left it in reservation mode it only took a few minutes to pick up again.  I didn't leave it in reservation mode the next time I drove and it never lost signal (maybe just chance).  I'll test it out over the next couple days to see how it goes.

I bought this alarm on eBay.  Would FirstTech warranty that, or would I have to return to the person I bought it from?  They do offer a 3 year warranty (the eBay person) that I still have the option of buying for like $15.