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@shicks surely the issue isn’t how long it lasts – it will always run out of power at some point, or even worse batteries loose capacity, what was working decays – the issue is how to reliably recover when it has run out of available mA. ?
The reliable bit – as in all engineering – is to add a buffer for real world component variations and that it just works for the “large power demand” when the modem turns on – across the expected usage of the battery. When Li-Ion batteries run down, their impedance goes up, they can supply less current at that voltage, and they need special charge management while they acquire a minimum charge .