I suspect that there are a few things in play here...
It's the wrong carpet for RC racing. Just because it is felt-feeling and looking means nothing. Unless it is Prima GT or CRC Fastrack, the chances are it is unsuitable for RC cars.
It has been polished through years of having bowls played on it. The polished surface of the bowls has polished the surface of the carpet fibres and so there's no grip at all for anything as light as an RC car.
I would get some additive and spray it on to an area of the carpet. Give it an hour, and then run a car over it. If that gives more grip, you know what to do. If not, your guess is as good as mine! HTH
