When a rubber roof shows black spots and if it is not something on the surface it may be the actual rubber roof showing. I always used a commercial rubber roof cleaner with a soft brush but over the years I began to see some black spots that were the actual rubber roof. I purchased the acrylic based rubber roof coating from Camping World and cleaner and recoated the roof as per instructions. The results were amazing and it was well worth the cost.
This may not be your case but I thought I would throw it in anyway.