Is Until his mother called him twice a correct sentence fragment?

You are correct! "Until his mother called him twice" is a sentence fragment.

Here's why:

* Missing a subject: It lacks a subject (the person or thing performing the action). We don't know *who* is doing something *until* his mother calls.

* Incomplete thought: The phrase only describes a condition ("until his mother called him twice"), but doesn't tell us what happened as a result of that condition.

To make it a complete sentence, you could add a subject and a verb:

* He waited until his mother called him twice.

* He didn't leave until his mother called him twice.