This is the use case:
I am deleting two posts from a user and want to see if he posted more on the next page. No, he did not, but the bar is gone to delete the original two. Perhaps as deigned but have to do "workarounds" to delete them. Check/uncheck on that page? Back button? Thanks for the post, I thought it was a bug and remembered, that's how it currently works.
I would think it would stay intact as, it's pretty common to navigate pages and get to where there is none needed, but you need to moderate what you already checked.
I do agree it would be more user friendly if the bar stayed at all times, it was only today I realised that button in the above screenshot brings the bar back up, I thought it would check all the threads on the page. I guess it hides it in case you navigate to a totally different forum, but it's not super clear how to get it back without selecting more threads, that icon is very small and unassuming.