I noticed that when checking in online the boarding pass says "Added to First Class Standby", but when I reprint my boarding pass at the kiosk, it no longer says that. When I online check in again, the BP also doesn't say I'm on the list.

Does that mean I am no longer on the standby list? or F is full? or something else?

I would think that I should be on the list until the flight departs.