Open files in MySQL increasing over time, eventually causing it to stop accepting connections
We've followed the advice at What value of thread_cache_size should I use? and increased thread_cache_size, which was one of the suggested changes at MySQL crashing at about 70k open files as well. This seems to have stopped Open_files from increasing as it was before (it was increasing by 1 every few seconds).

I believe this makes sense: if the bug is that threads aren't correctly releasing certain files, then creating less threads (reusing more cached threads) could result in less files being left open. This is of course just guesswork of mine.