A fully charged 3.2 V DC cell used to power a 3.5 V DC light string gets discharged in 2 hours
When it's first hooked up with a full charge, a typical battery's voltage will start off above the &quot;rated&quot; voltage, quickly drop to a value around the rated voltage, and then slowly drop until it's mostly discharged when it will nosedive.  It looks like you're seeing the initial high voltage (which for LiFePO4 is around 3.5V) and then the dimming as the battery drops to around 3.2-3.3V which is the rated voltage.  The cut-off at 2 hours is likely due to the voltage of the battery dropping to a point where the regulator that powers the LEDs can no longer function.  The solution is to use a DC-DC converter that can power the LED string at a constant 3.5V even as the battery voltage drops below this.  Something like this: https://www.pololu.com/product/2869 would fit the bill nicely.