Now that T232960 for "QuickStatements batch running in background not stopping with the stop button" is marked as resolved, I think a problem that I assumed to be related but is not resolved as of now needs its own ticket, so here we go:
Sometimes, a QuickStatements batch running in the background is stopping without me (or an admin) telling it to do so. A current example is batch 18726. When this happened in the past, the batch was usually resumed when I pressed the "Run" button again, but this does not work here.
Also, I think there were a few other similar cases recently, but since the interface only shows the most recent 20 batches and does not provide a way to browse past batches that have things like errors or "not done" edits, I have no easy way of finding such examples right now.