My first thought is that maybe the theme requires a lot of memory and it just so happens when Connections is activated, it pushes it over the limit and the result would be the same if you activate another larger plugin. So, that said, my first suggestion is to try increasing the memory allocated to PHP. Here’s an excellent post on how to do it. Since every web host is different, the method that will work for you will depend on the host server config. My suggestion is to start at the top and work your way down the list. Generally I recommend setting 128MB as that should, in most cases, provide plenty of headroom but try going straight to 256MB.
If changing the memory does not fix it, then I’ll need a copy of the theme for further debugging. If there ends up being something I need to address, I’ll fix it. But it could very well end up being an issue with the theme and not Connections.
Hope this helps!