I remember one phone I had that would sometimes hang and reboot when it was running low on power. It didn't do that when it was brand new. I always chalked it up to battery degradation.
Electrically, a battery looks like a voltage source with a resistor in series with it. Series resistance makes voltage fall with rising amperage. The resistance gets greater as the battery ages, until the voltage regulator can't smooth out the voltage jumps anymore, disrupting the digital logic circuits.