If the pin that adjusts the time on a wristwatch falls out on shabbos, is it permitted to push it back in to allow to watch to continue functioning properly?
My understanding of what you are asking is that when the pin is pulled out the watch doesn’t work. Since the watch isn’t presently working, the pin may not be pushed back in since it makes the watch function, which is fixing the watch- (Tikum Mana, Makeh B’patish). Not only that, but the watch is also muktza, since right now it has no Shabbos use and is considered broken, unless the watch is so nice that it is also used as a piece of Jewelry.
M:B 338-15, 308-168, Shmiras Shabbos Khilchoso 28- 20, 26.