Eep, that stinks.
Maybe there could be two warnings prior to restart--one at 5 minutes, one at 1 minute--as a precaution? Knowing the time and getting a 1-minute warning is helpful, but either is easily missed by a player thinking, "Ah, I'm safe here for the moment, I can go grab a coffee/use the restroom/check my beeping e-mail, won't take but a minute or two!"
