Not sure whether it happens to Bardin in all of his careers since I normally play him as Outcast Engineer.
To pick up the 2nd grimoire, if one fails to jump on to the window sill involved in the jumping puzzle, one has to climb up the ladder on the ground floor to try again. It is on this ladder that Bardin sometimes “bounces” up and down at the top but is unable to get over it, so jumping off the ladder and retrying usually works. I do not remember him getting stuck on any other ladders.