I was experiencing this the other day on phpBB.com when changing the order for the new Extension release forum. Had attributed it to some other weirdness there but evidently that's not the case.
My VM running Windows 7 and IE 11 has had some slow connectivity issues as of late so that might be the main contributing factor. When I would click on the forum up or down arrows the screen would change the order but the actual order was not being changed. So on the surface it appears that the request is not going through or is timing out while the order on the screen is changed. Since there is an AJAX call here the order changing should be attached to the success portion of the call with a "loading" indicator showing as it appears that this might be happening outside of the AJAX call, although I haven't looked closer at what the forum sort function is doing.
I'm thinking that another factor here might be the number of forums. We have a LOT of forums (200+) so that might be contributing to the problem, though not sure what the OP has for total number of forums.