It could he any number of things, unfortunately. It sounds as if it, or a driveline vibration, might have been present to a degree since you bought it, is that correct? The fact that new discs/pads seems to cure it for a while, though, is odd.
Damaged front wheel? - how bad? That could point to an out-of-true wheel, but doesn't explain why it's okay initially, likewise if one or more tyres had flat spots, or internal structural damage.
It's almost impossible to suggest the cause of the problem, without somebody driving it or physically checking it, ie suspension damage when the wheel was damaged, faulty brake-assistance/stability system being partially activated, faulty/loose driveshaft/diff., cracked spring etc..
Did the dealer carry out a Star diagnostics check, possibly not for a perceived
brake disc problem. It won't highlight mechanical faults as such but might show up electronic faults, ie brake/stability systems.
Did the dealer drive it in order to replicate the problem, or just replace the discs each time?
Any unusual tyre tread wear patterns?
As already suggested, MB customer service worth a try but a potential difficulty is that as you haven't owned the car from new you can't be sure of its history prior to purchase and if it's found to be a non-warranty issue, it could rack up time at dealer rates. A good indie is an option if MB customer services aren't forthcoming but the downside is warranty/goodwill. Catch 22.
Has a run-out check been done on the discs, and also done as soon as the new discs were fitted? I'm not sure how the hub could be out of true and I'd be surprised if 3 sets of discs have been fitted without the mating surfaces being clean/clear.
I presume that the A45 has electronically controlled dampers, if it's worse in Sport mode, faulty damper?
Sorry, no answers but the 'temporary' cure is puzzling and could point to something suspension/driveshaft-wise being slightly out of true which gradually affects the disc once it's put to use, but that's pure speculation, and doesn't seem to make sense.
Please keep us updated.