What happens if my wealth goes below the Nisab for part of the year — is Zakat still obligatory upon me?

If wealth goes below the Nisab at any given time during the year, then Zakat is not obligatory. You are liable to pay Zakat once you have reached the Nisab threshold and have maintained that amount for an entire lunar year. Once you have reached the date from which a full lunar year has passed, only then is Zakat due.