First of all, Mibew Messenger 1.6.4 is outdated, flawed, and unsupported.
Second of all, there are a dozen of reconnection-related posts around here. You really should have used the search.
Ask your hoster about the limits. Increase the values of 'Chat refresh time' and 'Operator's console refresh time' in
Settings ->
Performance.
Third of all, obviously you're experiencing some troubles with your hosting environment. Maybe it's somehow messing up with sessions. Or with incoming (proxied ?) requests. It has nothing to do with Mibew Messenger, so you'd better to ask the technical support of your hoster.