Naval officer are never discharged from inactive reserve. They must explictly request release from their Naval commission, from the SecNav under authority of the President.
Even an officer who has long been retired, if found to have been involved in some matter for which the Navy is investigating, may be re-activated for the time
Yes, if they still remain in the Inactive Reserve and have not been reslease from commission by SecNav.
there does not seem to be any evidence on the Internet, yet, of a related certificate of discharge.
Yes there is. It's dated Feb 1978 and I posted a direct link to it above. Why he waited until 1977 or thereabouts to request a release from his commission is unknown, since the request itself is not posted anywhere.
Possibly, he did re-up and so he did an extra 6 year hitch in the inactive reserves.
As I said, commissioned Naval officers don't re-up. They are always and forever Inactive Reserve until they request otherwise.
what was happening, such that Lt. Kerry did not receive a discharge in December 1972.
Because he disn't request it until later, probably 1977. Why he did that is, again, anyone's guess. There may be a good reason why Kerry chose to wait that long, or not. Or it may simply have been procrastination on his part.
The 180 would answer it, because his request would be in the file.
On the other hand, the Navy, the Secretary of the Navy, the President, personally or in effect, may have elected to administratively separate John Kerry, for cause, from the Navy, and then, he would also have received notfication of his separation, though, then, there may be some exception on the arrival of any certificate of discharge --- that is, it, the certification and certificate, may be "administratively hung up" and take some time getting to John Kerry.
Possibly, that 1978 certificate of discharge, is the said, same document that "took some time."
On the Internet, there is no evidence, yet, of the moment of John Kerry's request for separation, if any was made, or of the administrative and legal matters which may have "hung up" the proceedings.
On the matter of "re-upp"'ing, yes, Navy officers do; they enter agreements to serve periods of duty obligations.
We used to ask each other, "Are you staying in?" "Will you re-up?" Enlisted. Officer. We knew the distinctions, but used the same terms.