SureAI

I was about to take the oath as a keeper when I got a notification that a quest concerning Jesper was going to be "terminated / failed."

So I backed out and went to the tavern to meet him. Turns out there was nothing further associated with him--he was leaving.

So...was I supposed to beg him to stay? I got the feeling there was something else going on there but I don't play for that team and didn't pursue it. Was that the only purpose? Does the questline end there?

When exactly did you get the notification and when did you back out of the quest?
And what did Jespar say?
A savegame before becomming a keeper would be helpful.

The quest-line warns you at the point of no return.

Unless your going for the romance option I would not worry about it, plus I have no idea how those are triggered anyways.