There are a lot of websites that use automated judges. DC was founded as an alternative, so ALL games are run by humans. If you want automated games, go check out one of the other sites. Please don't take what I've said as a brush off. It's sort of like going to a butcher for pears. "That ain't what we serve here."

As for grace period, a few (very few) GMs do this. I used to do it, but it can get complicated (can another player use a grace period to update his orders, what if two players are late, etc) and so now I send reminder e-mails 24 hours before the deadline to players whose orders I'm missing. Most GMs send at least general reminders.

As for holding the game because of a single missed turn, Diplomacy is supposed to reflect the real world, and in the real world sometimes people are late. This doesn't really create "cheap wins", as it could happen to anybody, and at any rate you still need to fight with the other 5 players. They will ALSO try to exploit the situation.

Also, holding games up ruins the sense of pace - I've seen multiple games die while waiting for a replacement, even if its only a day or two. Everyone plays it out, but its more out of a sense of duty than a sense of fun.