I admire your degree of engagement with language, deconstructing it, rather than just mechanically memorizing it. And you’re absolutely right! All of the German phrases that contain "noch" have to do with ongoing time (i.e. still/yet/again ... ) And, because “mal” means “time/instance/occasion, together this phase yields something like: “still more / more yet / yet again / once again / one more time” you get the idea ...

Of course there are other ways to translate it; once again as you said, one more time, and so forth. Now, nochmal, or more properly spelt, noch mal is a colloquial shortening of noch einmal which is just a synonym of nochmals. I'll cite some examples for usage but you're not in for a surprise here ;)

• gehen wir noch mal raus zu den Hühnern? - are we going out to the chickens again?
• ich komme nicht noch mal zurück - I won't come back again
• kann ich's bitte noch mal versuchen? - can I please try it again?

and the full form:

• er küßte sie noch einmal - he kissed her once more

and nochmals:

• ich danke Ihnen nochmals für den Bericht - I thank you again for the report

From my awareness, the word "Nochmal" means "again" or "once more." It can also mean a few other things as mentioned already. But this is one of so many examples of how translation doesn't work the way most people think it does. The more German I learn, the more I realize how the German that's translated into English doesn't make sense. Sorry if I went off topic, but I couldn't help but think this while reading this discussion.

The alternative is noch ein mal, means once again. Nochmal means again, and of course the other examples are true, :-)

hi+