Why does "mattaṭṭhaka" mean "short-lived"?

The term “mattaṭṭhaka” occurs in the Tipiṭaka only in MN28, where it appears in the genitive case (“mattaṭṭhakassa”). As far as I can see it is always translated by a term meaning “short-lived”. That certainly fits the context:

What then of this short-lived body derived from craving? Rather than take it to be ‘I’ or ‘mine’ or ‘I am’, they still just consider it to be none of these things.
Kiṃ panimassa mattaṭṭhakassa
kāyassa taṇhupādinnassa ‘ahanti vā mamanti vā asmī’ti vā? Atha khvāssa notevettha hoti.

I have no reason to doubt the translation, but I don’t see why the word form should mean “short-lived”: hence my question.

I guess my problem is that I can’t seem to parse the compound to mean “short-lived”. The best I can do is “matta-ṭha-ka”, where “matta” is associated with mattā, which has the Sanskrit form “mātrā” which could mean a very small quantity as opposed to some unspecified quantity. If that is the case we would have something like “short-stand-ing”, meaning “short-lived”. But that seems a bit of a stretch to me.

So, Why does “mattaṭṭhaka” mean “short-lived”?

David.

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