I found a knowledge base article that appears to describe your issue titled DVCS Github sync failed. It lists the Cause and Resolutions as follows:
The DVCS plugin uses the eclipse git plugin to access GitHub. The git plugin from eclipse keeps track of the rate limit for a connection, but doesn't take any action if/when it reaches the limit. If the next synchronization starts before the rate limit is reset, the synchronization will fail again. When the synchronization reaches the rate limit, the currently processed message will fail and attempted to be applied in the next synchronization.
For JIRA Server, you can try to add the dvcs.connector.pr-synchronization.disabled dark feature to disable pull request synchronization as a way to reduce the initial sync load on GitHub. Then, re-enable that feature later when load is back to normal.
For JIRA Cloud, you can request that support verify the API limit is being reached by checking your JIRA logs or if you already suspect that as being the root cause, keep watching JSWSERVER-14299 - Receiving "Sync Failed: API Rate Limit Exceeded for <user-id> (403)" when attempting to add a new project Resolved for updates.
In addition, there is also a bug that you can find at JSWSERVER-16243: Upgrading Jira to 7.6 causes DVCS to fail on MS SQL environments.
The workaround is listed as follows:
It might be possible to migrate the Jira database to a different database type such as Postgres or MySQL as a means to get around this. However this is not a simple work around to follow and could take some significant time to process.
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