Why does my fireplace pilot light go out when I turn on the flame?
Is the new log set the same btu? If your new assembly is using the original gas valve with a larger btu burner there may not be enough back pressure to maintain the pressure needed for the pilot. I have seen the supply line being two small for the size burner have this same problem. 
That case a 1/2” supply line to a burner that was 10000 btu larger.  the owner wanted the larger burner for heat when power was lost ,  To solve the problem we tried a new regulator before he told me he had increased the burner size. Upsizing the supply line to 3/4 and it worked fine. The original gas valve was large enough but the smaller supply line caused the problem. 
If your new log set is larger you may have the same issue, reducing the jets size or increasing the supply size may solve your issue.