"When does a MovieStock® cash out?
A MovieStock delists and cashes out from the market on the first business day after its fourth weekend of wide release. If the film remains in limited release, the MovieStock cashes out similarly after 12 weekends. The MovieStock for a film that goes straight to video or television cashes out the week the film debuts in the U.S. at H$0.00."
https://www.hsx.com/help/?page=faq
No, you do not have to re-buy a movie stock every time its stage changes.