With 30 seconds, they are getting offline even if they are with the visitor's window opened. I've seen and tested that. So, the visitors on the website get the offline button and cannot talk with my operators. The operators still believe they are waiting visitors, but no one will ever appear because the button is showing offline and redirecting visitors to offline messaging (by e-mail).
Then your operators have connection problems. As I told you before the original problem can be fixed by setting moderate value to "Operator online time threshold" option.
If we talk about connection problems then I have no idea what is broken. So, if you want to get help, you should provide as many information about the problem as you can. This info must include at least:
1. Exact version of Mibew you are using.
2. Type of hosting (shared, VPS, VDS, ...).
3. Name and version of OS which is running at your server.
4. Versions of PHP, Apache, MySQL.
5. List of browsers (with versions) where the problem exists.
6. Contents of apache's error log.