My 2003 GMC Yukon XL Denali low beam headlights do not work. They went out, then a few days later worked again, then went out completely again. I checked the fuses and replaced the low beam relay in the fuse box under hood. The high beams, parking lamps and fog lights all work fine. What should I try next?

The problem is likely your multi purpose signal light switch. If you take the lever and move it from hi to low beam will the low beams come on? It is common for this multi purpose (real expensive ) switch to fail after a period of time! The steering wheel may have to be removed, to change it. The air bags will also need to be disabled so as not to active them while removing the switch.