A320 flight crew reported having a stuck mic which prevented them from receiving a takeoff clearance.

Narrative

We had vh1 transmitting ecam flash twice on arrival into ZZZ but cleared itself immediately. There was a stuck Mike all the way to landing. On the ground; no stuck Mike at all and so unsure if it was us. Maint checked and found ops check good. We taxi to rwy to take off; no issues. Told to line up and wait on rwyXXL. We do. Then we are told cancel takeoff clearance; stuck Mike. We never heard (received) a take off clearance. Then we are told to take off and we do with no issues. We had issues on the climb out with stuck Mike; with departure finally telling us that it was us; first time this was confirmed. We still had no idea what was causing it and searched manuals all the way to ZZZ1; but no further ecam this leg. On the downwind for ZZZ1; we thought the culprit was the captains radio trigger switch; which appeared to be rattling. On the ground; no issue taxing in. We wrote up the Mike issue again; this time directing maintenance to the switch. After an hour; they determined the switch was faulty and rapidly failing and disabled it. We had no further issues after this. This issue took 2 legs and 2 separate maint people to determine where and what the inconsistent problem was.