Next session most of my PKs will see their squires turn 21. I know that typically a squire will leave the knight's service to be knighted himself, but some may remain as professional esquires. Naturally my players would like to keep their experienced squires, especially since they suspect there are some battles coming up. The Book of the Manor has a rule for determining whether an esquire leaves service, but I was wondering how other GMs you determine which squires stick around to become esquires?

Given that we're still in the Uther period, and shortly will enter the Anarchy period, Logres needs all the knights it can get. So everyone in our group loses their squires at 21 right now.

If your players have not roleplayed any discussions with their squires nor have indicated before this any interest in their squires then I'd take them away. Keeping them from becoming knights if they can is dishonorable.
However if they have had scenes where they have bonded with their squires or if they have shown a particular care/love for a specific squire then I'd give them a dilemma scene where they might get to keep them, maybe just a for a year or two.

Simply from a roleplaying perspective you should remove all non-special squires when they turn 21. But if they have been interesting and have gotten lots of attention then that is a squire that can be used as an esquire for many sessions.