Service engine light and gas tank

The other day the service engine light came on when I started my 1999 Buick Century.I filled up with gas the next day and the light went out.Okay,maybe the gas cap was loose,I thought.I drove all day,and when the gas gauge went below half a tank the light came on again.I filled up and the light went out.This has been going on for several days now.Every time the tank goes below half full the light comes on.

Anyone have any ideas?A new gas cap comes to mind,but I'm not sure.

Next time the SES/CEL MIL light comes on get it scanned with an odb-ii scanner to see what DTCs are stored. Places like Autozone will do it for free. Then post the code(s).