Hi Rasul,
[quote user="Rasul Kishov43"]Am I right to think that this happens because reverse motor current even higher then 1.6A and overcurrent protection doesn't save the chip?[/quote]
The reverse motor current is probably not the problem. The device is designed to handle currents higher than 1.6A for short periods of time. The problem is more like due to a voltage surge on VM when reversing currents.
Do you have a local 10uF cap on the device VM? If not, please place one close to the DRV8835 as shown in the datasheet. Also, please look at the VM voltage with respect to GND at the pins of the DRV8835 when reversing currents. If you are experiencing large voltage spikes (greater than the abs max voltage), you may need more than the 10uF capacitance.