Is it acceptable to drop "having" in "having to do with?"

I encountered a problem having to do with the connection…

vs.

I encountered a problem to do with the connection…

Is the second option a legitimate expression?

I think that either of these is acceptable:

I encountered a problem having to do with the connection.

I encountered a problem with the connection.

The variant that includes to do but not having may be used by some people, but it's much less common.

To do with exists, though in my (US) experience it's far less common than having to do with. (But in the particular example you give, I encountered a problem having to do with the connection, I agree with RegDwight's comment that having to do should be dropped altogether.)