A 503 Service Unavailable Error is an HTTP response status code indicating that a server is temporarily unable to handle the request. This may be due to the server being overloaded or down for maintenance.
This could happen when you purge the cache, “if” you have too many cache files on the cache directory. In that case, it’s not the plugin causing the error, it’s the server that cannot handle deleting so many files.
Whenever you purge the cache it still needs to read all cache files, and delete one by one. If there are lots of them and the disk / server is slow, it exceeds the limit set on the server simply because it’s trying to read those files, not exactly doing anything about the files.
Slow disks are common on scalable hosting, or remote storage servers.
It doesn’t matter how reputable or well known the providers are.
Pantheon for example, is a well known hosting provider but their disks are some of the slowest I have seen. Unfortunately, that is the price to pay for scalability on many of those managed providers.
You can ask your hosting to manually delete the FVM cache folder or you can do so via sftp/ssh, or using your control panel from your hosting if that option is available.
In addition, you need to read the faqs:
https://www.ads-software.com/plugins/fast-velocity-minify/#faq
If you have a lot of cache files, likely one per pageview, you most likely have a dynamic css or js file, or some piece of code that is being merged but “changes on every request”, and that needs to be excluded.
Otherwise, FVM will see different code and create a new cache file every time it changes.
FVM is a plugin for developers and advanced users.
You need to at least, be able to see what kind of cache is generating and configuring it properly.