Well, Connections on its own does not interact with the WP login and does not do any redirecting. The only exceptions would be with Link and Form extensions. Link runs a quick little check on login to link a WP user to a Connections entry, no redirects. Form, there is a redirect option, but that only has an effect when adding/editing an entry to Connections. Neither would cause a redirect on login.
I can’t really give any thought on a solution because I do not have enough info. And, I have to say, with I do know, it is not likely related to Connections.
My best suggestion for you is to temporarily disable Connections and test logging in. I suspect the issue will remain, eliminating Connections as the source of the issue. If the redirect loop does go away after deactivating Connections, then I’ll need a temp WP admin login so I can take a look first hand because there should be no way for Connections to cause a redirect.
Hope that helps! Let me know.