The person who initially installed the Recurly-Salesforce integration is considered the sync user, but this can be changed if, for example, that person is no longer working with your company.
To do this:
Go to your Salesforce org -> Profiles -> System Administrator -> View Users -> Click New User. Once you have added a new System Administrator, remove the old one and just leave that one system administrator. Also, make sure that the user with System Administrator profile has all Recurly permissions enabled.