I had a problem like that on a 90 hatch.. the alt wasn't charging full power.. but it would charge the batt enough to not kill the car while driving. Battery light would come on after driving for 10 mins and the lights/radio would die. Bass from the system would make my lights cut off and make the car skip and miss. lol
Get the batt tested and see if it's still holding a good charge.. then try replace the alt.. and if it doesnt fix it.. return it and then start checking grounds. GL