I think you can follow NFL rules where if the pick doesn't come in the allotted time (in this case, 4 hours), you can go ahead with your pick. The team passed over can still submit their pick as well. It's whoever posts here first get the pick. [I would prefer it if teams here had less time in the second round to submit their picks, like 3 hours, and even less in the third round, but I understand people here have lives, so they can't always be here to monitor the thread.]
[Also, the team picking before Buffalo in every round here gets 8 hours actually, not 4. This is because the Buffalo poll must last 4 hours. Therefore, if the team before Buffalo misses their pick in the 4 hours, they still can submit it in the next 4 hours before the poll is finished.]