Reply To: searching not work

I did take a look, something seems to be stripping or removing the query variables Connections requires to function. This will break a lot of plugins, not just Connections.

The first thing you need to try is deactivating all other plugins. If the issue resolves itself, then you know one of the plugins is breaking basic WordPress functionality.

If the issue persists, then it is likely the theme. Temporarily switch to one of the default themes like TwentyTwelve. If that fixes the issue, then it is the theme breaking WordPress.