Clock Question

>!Spoilers about puzzles and prizes involving the clock tower:!<

>!I got the sanctum key for solving the clock tower puzzle, but wasn't able to use it and lost it from my inventory the next day.!<

>!I've since returned to the clock tower, hoping the key would respawn, but the secret door didn't open up as I stood inside the clock tower at 1:30.!<

>!Does the clock tower door open back up again? Do I need to stand at the top of the tower instead of the bottom? Is the key lost forever?!<