The concern may be that there could be undiscovered vulnerabilities in the service and releasing the source before shutdown could make it easier for malicious actors to discover those vulnerabilities and compromise user data.
Yes, that's the rationale. A customer has asked about getting access to the source ahead of time and I'll try to make that work.
Given your setup would it be easy to make a data exporter/importer? That way you could give them the data and shut down before opening the source.
Placemark was built around that idea - all the data is easily exportable & importable in many open formats. It should be straightforward to move to the open source version or other tools.
As I mentioned in another comment, perhaps you could invite current users to a private repo, and then make it public at the business EOL.
If it’s open source, a private repo is not protection. Free software licenses allow for unlimited redistribution.
You don’t need to apply the license until after the public release, before then it would just be sharing code with your customers under whatever agreement you want