outlook 2010 disconnects from exchange server the moment outlook anywhere is configured.

Some time Due to network connectivity issue. You can ping and telnet the your exchange server with port 443 or 25. 

check out link below it might help:

https://support.office.com/en-ca/article/Use-Outlook-Anywhere-to-connect-to-your-Exchange-server-without-VPN-ae01c0d6-8587-4055-9bc9-bbd5ca15e817

Hi,

What version of Exchange server are you using?

Did you get any error message when it failed to connect to Exchange?

Please first try using the Remote Connectivity Analyzer to check if the Outlook Anywhere settings are correct:

https://testconnectivity.microsoft.com/

In addition, if you installed Microsoft Exchange 2010 Service Pack 3 (SP3) in an Exchange Server environment, please have a look at the following KB article and check if it applies:

https://support.microsoft.com/en-us/kb/2832198

"Assume that you install Microsoft Exchange 2010 Service Pack 3 (SP3) in an Exchange Server environment. There are many Outlook Anywhere (RPC over HTTP) clients in the environment. When the Outlook Anywhere clients try to connect to the Exchange server, the Outlook Anywhere clients are not connected."

Regards,

Steve Fan
TechNet Community Support