What do you call a form of government where the regent never dies?

single-word-requests government

If the ruler never dies, then it really is a mon-archy -- rule by one. All that is required is a single rule who reigns for life (or until abdication).

Nothing in any definition of "monarchy" requires any form of succession, and indeed there are many fantasy monarchs that are immortal.

Defintions such as the one from Merriam Webster are typical.

undivided rule or absolute sovereignty by a single person

Also, as Wikipedia points out, monarchs can be elective as well as hereditary.

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