As far as I know, normally we don't have to restart Outlook to restore the connection with DNS round-robin in place. For more information, you may refer to the Outlook client experience mentioned in the following two blogs:
- Exchange Server 2013 Client Access Server High Availability
"Without the aid of a load balancer the Outlook clients takes about 20 seconds to time out and then re-establish connectivity to the other IP address..." - Exchange 2016 DNS Round Robin Load Balancing
"From the point of view of Outlook, nothing was noticed. Outlook was responsive throughout the failover and in fact did not disconnect."
(Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
That being said, I'd like to suggest checking the configuration steps described in the links above to see if anything has been missed. Also please try to install all available updates for the Outlook clients and see if there would be any improvement.
Besides, as noted by Robert and the official article he shared, while we can use DNS round robin, a true load balancer is always recommended.
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