When adding a Google Analytics account to a Web Presence you may encounter the above error if your Google Analytics Account has authorized more than 25 profiles within gShift. This limit has been put into place by gShift as Google maintains an undocumented threshold at which API access to Google Analytics profiles is revoked. The standard threshold is 25.
The solution to this error is to share access with another email address for the account you would like to set up and use it instead. This will allow you to authorize the Google Analytics account.
However, if you have established another threshold with Google, please contact firstname.lastname@example.org to have the limit manually adjusted in your gShift Agency account, which can be processed within 1 business day.