I've never really tried to stand for longer than necessary. And I would argue that simply saying "standing" while riding doesn't really describe a single aspect rider posture.
In other words - your questions ignore at least one important distinction of non-seated bicycle propulsion.
In some conditions I will stand and pedal to gain additional leverage - using handlebars with an upward force - to incerase pedal pressure.
I also stand while "leaning" on my handlebars. In this case, I could probably ride for a long period.