Keep/retain a syslog at lowest level possible even after a restart

Over the last several days, my phone suddenly started giving me a problem. It gets into a restart cycle - there is no pattern of when this problem occurs. It's very random, also the number of restarts in each instance is variable. I did factory reset twice (including cache partition clear) and hard reset (from recovery menu) Now I see some reduction in the problem, but it's not completely gone. It's my gut feeling it's a software issue. Is there any way to keep debugger logs on at the sys level so that next time a problem happens and after a restart, I might get some clues?