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Any computer, including servers, experience a slower than normal start up time upon the first restart after installing Windows Updates.
As part of the start up, eDiscovery's executable (EsaApplicationService.exe) checks the status of MySQL. Windows Updates causes MySQL to slow down which causes EsaApplicationService to interpret this as "not running", thus eDiscovery does not start as quickly.
To fix the immediate problem, start the EsaApplicationService manually in Services.msc on the server or through the Clearwell Utility on the server desktop.
Once the EsaApplicationService is started, the eDiscoveryUI should be available in about two minutes and log in should be available within 5 minutes as normal.
To prevent this from happening in the future, set your Windows Updates to automatically download but manually install.
Install updates during some scheduled downtime when all eDiscovery jobs are stopped and all users are logged out.
After the server is updated and rebooted, manually stop and restart eDiscovery services with the Clearwell Utility one time. Once services, start you should be able to log into the eDiscovery UI as normal. This will have to be repeated each time you install Windows Updates.