a pit usually dont have a lot of energy to run a long way to the bay and then catch and hold for a long time while you get there.
I always hear folks say that, but I've never seen it myself. Those dogs were bred for over 100 years for animal combat that sometimes lasted for more than an hour....
Back to the original question...for me it's situational. One place we hunt, you purty near have to turn them loose at the first bark...those are some running swine on that one. Most of the time we turn them loose when there's a solid bay, and follow them in. As far as how long they stay caught; usually no more than a minute or two...again, it's situational depending on where the bay is, brush, etc.