Hi @Josh Roberson ,
Welcome to Microsoft Q&A Platform. Thanks for posting the query.
This seems strange and we have not heard this kind of issue in recent times from any customers. I tried reproducing by adding, modifying and deleting global parameters in data factory connected to GIT and I did not see this behavior. Since it seems specific to the data factory, can you please share details of data factory name and region. Also, can you please check if any deployment is happening on data factory at that time because with global parameters the GIT configuration is not present in the ARM templates and this can cause GIT to be removed as per the document.
Please let us know these details to proceed with further investigation.