Another possibilities:
Cultural - having a single child to join estates
Biological - Longevity comes at a price.
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Possibly, but to fair I don't think there is a reason. The shire is similarly inexplicitly underpopulated when hobbits have been peacefully having large families there for 1400 years!
Perhaps all that magic is reducing fertility rates?
After all, magic requires power, sometimes quite large amounts, and no power source is to be seen. This means it's either beamed, or otherwise dispersed through the environment. This could have negative implications for health and fertility.
Or a more sinister reason: canonically, magic is powered by sacrifice - and most powerfully, human sacrifice. Sure, Tolkien skips over the child-snatchers, the sacrificial altars, the charnel-pits behind the Valar-temples, but we well know the true cost of the Numenorean theocracy.
This wouldn't explain the low population of the shire. (Unless there is a "The Time Machine" type scenario. :( )
Well maybe after the more fanatical followers couldn't follow through on the demanded blood/power/life offerings the powers that be continued to levy their sacrifices in an indirect way, that manifests itself as low birth rates or particularily high infant mortality?