Mal is the expert on this. But, with his assistance, here is what I think are the rules of the road. If by permanent residency you mean gaining "Belonger Status" you will be disappointed as it takes about twenty years before you can even apply.
We are officially "Non-Belongers" and have a government card to prove it.
Non- Belonger status is granted to people who own property in the BVI. With a Non-Belonger Land Holding License you are allowed to stay for six months without going back every 30 days to C&I to extend your visa.
I am advised that after six months, you are not supose to be allowed back into the territory until six months have passed. In theory, going to St. Thomas for a few nights doesn't allow you to skirt that provision. But, I 'm pretty sure that it is skirted frequently.
The right way to do it is the way Mal has done it, which is to apply for a Right to Reside Permit. He was able to get through that process relatively painlessly, by island standards. I think it involved a number of trips to C&I in addition to the paperwork.
But, I envy you. We still haven't figured out a way to extend our stays beyond three weeks. Best of luck!