Hi,
Replace R15 with a 10uH inductance.
No, joke aside.
It's impossible for us to give help without knowing your circuit and software.
You need to debug the circuit:
(Two main reasons for your problem: power supply and software)
You need to verify that the power supply is stable and within specified values .... all the time.
Simple method to find out whether there is a software problem:
Replace your software with one that just toggles an output pin once after RESET. Then connect a scope or pulse counter to this output to detect whether the device unconditionally resets or not.
Klaus