After some experimenting it seems that the situation improves when I call task.mark_started(force=True) before each task.upload_artifact() instead of just once in the beginning of the script.

Seems there are two approaches, either "revive" before each upload, or somehow keep it always "Running", do you have an idea how the second approach can be achieved? (I did not call task.close() or task.mark_*() anywhere).