Will a slow or failed check pile up or break the schedule?

No. The app only schedules the next check after the current one finishes, so slow checks can't stack up. If a check fails (e.g. a network blip), it waits a bit longer before retrying and gradually backs off, then returns to your normal interval once it succeeds. A check that comes back empty or incomplete is treated cautiously and ignored rather than wiping your list.