Battery drain on 6.9 diesel

We have a 1984 f350 6.9 diesel. If
she sits for a day she won't start. We
go through about 6 batteries a year.
They lose the ability to start the
truck. We have changed the
alternator and we disconnect the
positive terminals on both batteries
any time it will sit more than a couple
hours but it still loses battery charge
(11.7 and 11.6 this morning), enough
that we have to jump it. The current
batteries are about two months old
and when new have no problems
starting the truck.