I've seen a delay of of 8 hours before. it came through at about 1000, for an airborne time of 1800ish. We all just cracked up because the a/c subjected to it was one of those who just missed his original slot, so we requested next available for him, he got 2 hours delay, we tried hard to improve it for him, and got it down to 45 mins delay. As he was taxying out, he went tech, so missed the 2nd slot time. An hour later he reported ready again, got 1 hour delay this time, and as he was just about to push back for that slot, a new plan came through that company had refiled for, with an even worse slot. Then Flow said he could go with no delay on the original route, but then immediately after that a new slot came through of 2000.
I asked if the assistant working the DSM (slot computer) would like to take the RT to tell the crew, but he declined. I'm not sure what happened after that, I went on a break. Although I did check and he was gone the next time I got up in the tower!
I can only surmise that his company were'nt aware that he was able to depart and had put in a changed off blocks time.