Citroen DS3 engine cutting out, idling rough, cruise control inactive, stop start inactive

A broad list of problems to try to pin down, but they do seem to all happen around the same time.
This problem intermittently comes, gets progressively worse over the course of weeks, gets really truly bad, and then from time to time goes completely.
*The engine idles rough: it will sit fine for a few seconds and then the revs will plummet for a second as though it's struggling to breathe before coming back up; during the worst phases the engine revs are fluctuating constantly.
*When driving, the engine will occasionally stop accelerating or decelerate for a second, and it has cut out and stranded me a few times.
*Whenever the engine is bad like that, the cruise control either won't activate, or it will activate and then suddenly cut out later on.
*During the bad phases, stop start won't work.
*On the worst occasion, it did give an 'engine fault' warning in the log.

The most confusing part is that when the engine fault warning was present and the engine revs were hardly reaching idle, the garage just did a diagnostic and cleared the faults in the computer, and since that the car has been absolutely fine until now. Clearing the faults on the diagnostic actually fixed it, meaning that they didn't know where to look.