The banishment system works by the seasons. If the current season's leader has
banished you, you are banished from the guild. Otherwise, it takes all other 3
seasons to banish you.
Therefore, if the spring leader banishes you but nobody else does, in the
spring, you are banished, and in all other seasons, you aren't.
Shinarae Lluminus
Also, banishment votes remain -- intentionally -- through elections. They
probably last through reincs, too.