At first I thought that it could be a circular ref problem, but then I read his description and that isn't what it sounds like. I would first go with the ->disconnect suggestion. I would then peruse through the code to look to see what other methods the dbh could be getting passed to. Undefing {dbo} or deleting it won't cause a copied reference elsewhere to get DESTROYED. I would guess another object or data structure contains a copy of the dbh - so that you will not be able to rely on implicit object destruction.

You could always call $self->{dbo}->DESTROY but I'm not sure that is best practice. I'd stick with the ->disconnect.