Certain vaults were equipped with technology to last them how long they were supposed to stay closed. some vaults were supposed to stay closed for 6 months. Other vaults like vault 101 was never supposed to open so it could stay closed forever.
It should be pointed out though, that the vaults that were closed for 200 years were supposed to test how long people could stay isolated, so they weren't necessarily supposed to be functioning efficiently the entire time. The control vaults were supposed to reopen after only 20 years.