This seems a little far-fetched, but is there any chance someone might have dumped motor oil or gasoline in those areas in the past? That will prevent grass from growing for years.
Regardless of what's causing it, if the spots aren't very large, you could try digging them out and replacing the soil. I would dig down about 4-5". Then re-seed.
Regardless of what's causing it, if the spots aren't very large, you could try digging them out and replacing the soil. I would dig down about 4-5". Then re-seed.