I had someone quit and pull four characters because their hold lapsed on the fifth and someone else with a great application submitted as soon as it expired. Three days later they flipped out and quit. And everyone in the community was sad to see their characters go but thought they made a fool of themselves pitching a fit.
If they can't get the app in before the hold expires and they can't contact you to at least ask for an extension, what makes you think they'll be reliable tagging in a timely manner? Maybe they had computer issues, but such is life. "Computer issues" are also a famous scapegoat for slow RPers. It's just bad luck if it really is a PC problem.
If the hold is lapsed they have no claim. If the player flips out, then you don't want that kind of drama. So long as your hold policies are clearly stated, fair is fair.