I had my fair share of dying BQ24650 chips.
Most of the time they stopped working after some voltage-spike on the battery-side. Either by suddenly disconnecting the battery (I wanted to simulate a loose connector next to a running engine and wiggled the clamp at the pole, causing some sparks), or when I connected a Battery-Pulser.
Most of the time one of the internal regulators of the chip died, causing parts or the entire chip to stop working.
In the end I switched to a different chip from Linear Technology that was also easier to solder.
What I would check in your circuit:
- Is there enough dead-time between the ON-Signal of the MOSFETs / Is there any overlap of HIGH-Level on the gates?
- Drive-Signals with nice sharp rising and falling flanks?
- Is there oscillation with just the battery connected? - Explanation: Current from the battery to the input capacitors stops rather suddenly when the caps are charged and could lead to a small voltage-spike due to the changing current in the inductor, which in turn makes the chip think there's a Solar-Cell connected, which then makes it start the battery-detection cycle that in turn shorts the battery, makes the voltage at the input drop, turns the switch off, turns the current-sink of the inductor off and voila: You basically have a parasitic Step-Up Converter with the sense-resistor as the current-limiter
This could be stopped by adding some capacitance to the MPPSet-Pin, as well as setting the MPPSet-Voltage high enough. - This could explain the way the resistor burned out: Short current-spikes that heat up the spot with the highest resistance.
I have to admit, the last point is a bit far fetched but I wouldn't rule it out