Thank you!Google searches suggest that "connection problem" is by far the more widely used term in this context. (But that's not to say that people don't sometimes say "connectivity problem" to mean the same thing.)
A connection is a link between two [or more] things, such as electronic devices.
But connectivity means the ability of one thing to connect to or communicate with another, rather than the connection itself.
Oxford definition of connectivity (in the context of computing):
capacity for the interconnection of platforms, systems, and applications.