Another option: look at the server-side changes that were made just before the slowdown occurred.
In my case, it was a set of plotting routines. I had added 3 imports. By moving those imports into the functions that needed them – by importing them only when actually needed – the other server calls went noticeably faster.
In other cases, it might be a new set of database operations. In those cases, caching results in anvil.server.session might speed things up a bit.