I had a bad experience with garage floor paint.
I did as it said on the tin and left it for a week before parking Archie on it.
The next time I took him out, the tyres sucked the paint off the floor where the tyres had been (only the back tyres fortunately).
I currently have carpet covering the bald patches. Grr!
Unfortunately this is the case with any water based store bought paint, you really need an epoxy based paint that you get online - must more expensive but durable and won't come off. Same stuff professional garages will be using.
Only issue is I doubt it will adhere to the old paint as well as bare concrete, but as you are only having issues where the tyres are then it could do the trick.
Otherwise cheat - and buy 4 x grey carpet tiles from B&Q and put those where the tyres sit.