You're in the realm of DM Fiat here. There's no reason a character couldn't dismiss a cohort, but I think you DM would be entirely within his rights to make sure there was a delay before a new cohort became available.
Personally, if the cohort was dismissed without good reason (in character), then I'd likely impose the 'Aloofness' penalty of -1 to Leadership score for the next cohort.
I would allow it. After all, druids can release their animal companions from service (pg. 50, Core Rulebook) and gain another one, so why wouldn't a (comparably) normal follower be able to be released from duty? :)
You're in the realm of DM Fiat here. There's no reason a character couldn't dismiss a cohort, but I think you DM would be entirely within his rights to make sure there was a delay before a new cohort became available.
Personally, if the cohort was dismissed without good reason (in character), then I'd likely impose the 'Aloofness' penalty of -1 to Leadership score for the next cohort.
+1. The "aloofness" penalty is a good idea!
I dismissed a cohort once. He'd been a long running cohort, too, and had become such an integral part of the party (plus, the party's only remaining cleric) that I had to release him in order for him to catch up to us in level (that -2 level cap becomes pretty bad at level 21...)
So sometimes, a leader has to let his people go, in order for them to find their own place in the world! (And that place was right with our party, as our healer - and equal.)