The problem is that this is not a single issue. "Connection lost" is a generic error message, which indicates that the service has stopped (crashed).
The actual cause is something different in each case, highly dependent on the data that was indexed and on the selected search ...
Submitting full diagnostic information to X1 may help with tracking the issue. See http://www.x1.com/support/x1_search_submit_case.html
One thing to try is to
1. make a backup of the "navigationtree.xml" file and the "saved searches" folder
2. delete the file and the folder (this will lose all the user-created saved searches, hence the backup)
3. Start X1 again and see if it crashes again. If it does not, then probably it is one of the saved searches that causes the problem. In that case we could help with pinpointing the problematic search and fixing it ...
Jogy