Is there a maximum amount of time heavy cream can be fermented?
It is the opposite. Fermenting lowers the pH of the cream, making it taste sour. And the time you can ferment it is limited by how sour you can stand to eat it. If you ferment it for too long, the taste will be simply unpleasant. 

Typical fermentation times are similar to yogurt and will depend on your culture. I ferment with thermophillic lactobacilii bulgaricus for about 8 hours. I don't know for sure when it will become too sour, you could just let a batch sit for longer and note the taste, until you see no improvement. If you use other cultures, you will have to inform yourself about the preferred fermentation times. Also, if you want a certain product, you will obviously be limited by how the product is supposed to taste, for exapmle creme fraiche is intended to be very mild and most people won't appreciate it if you fermented it to a more sour state.