Hello and thank you for your post. I am a master certified GM tech, with 15 years Saturn experience,and can help you to resolve your issue.
if this only happens when you are using the power outlet to power a cell phone charger, let me know.
if it happens without a cell phone charger, the wire harnesses inside the headlamps themselves need replacing
the sockets melt internally and cause an intermittent connection with the bulb.
there was a recall that had us add resistors to the circuit for the drl's which if never done, needs to be done. (call chevy dealer and ask them to check if the recall was done) but if it has been done, replace the harness inside the headlamp to fix this issue and put in new bulbs.
do NOT use just any bulb, use ONLY the bulb number for that vehicle as a different bulb may burn hotter and melt the socket.
if you are not 100% positive that the bulbs are the right #, buy them at Chevy and specify what bulbs you need and only buy the GM part # XXXXX

hope this helps