Is git's past history automatically deleted?

I don't think there is a version management system that automatically loses historical commitments, not just git.

Git does not remove any existing tags or branch history commits over time.
Any existing tags or commits that cannot be reached from a branch are garbage-collected and removed when you use the git command after a certain period of time (for example, 45 days). As long as you use it normally, you won't have to be aware of this automatic deletion mechanism.
For more information, check out git gc and git reflog.