Support pros are celebrated when we solve the customer's problem, but sometimes it takes more than one try. If you don't get it right the first time, you can still be the hero.
My car was in the shop last week. My windshield wipers stopped working, and that's a big problem here in stormy Northern Virginia. One harrowing drive to work where I was squinting through a downpour made getting my problem fixed a priority.
With this repair, I tried a new service shop, and I ended up not being entirely satisfied with the experience. Through a conspiracy of circumstances, I was without my car for an entire week. Parts had to be ordered, which I don't blame the shop for, but the fact that they kept bankers' hours made it difficult for me to pick up the car. In the end, though, I did get my auto back, and it seemed the wipers were working better than they had in years.
That is, until I actually had to use them in a rainstorm.
During a cloudburst, I fired up my newly fixed wipers and hit the road for my drive to work. As I got up to speed on the highway, a resounding smack started to echo through the cabin, in perfect time with the passes of my wipers. I pulled over and examined the windshield. Turned out that the smacking was the sound of my wipers sliding off the windshield and hitting the trim and driver's side door frame. The parts had not been installed to spec, and the wipers were extending further than they should. It wouldn't do to have the blades chip away at the trim around the windshield or the paint on my car's door. I immediately started making plans to go back to the garage and insist that my problem be fixed properly.
To be fair, I've been on the mechanic's side of this scenario as well. Sometimes PC techs don't solve the problem right the first time, and we have to take a second crack at it. Not fixing the issue can leave the customer unhappy. There are a few ways to salvage the situation...
Own the customer's inconvenience. Simplest comes first: if you didn't fix it right the first time, apologize. Admitting honest error won't harm your credibility, but refusing to accept responsibility will. Even if the user has a new problem that is actually unrelated to the previous one, use a gentle hand when explaining the nature of the latest issue. Nobody wants to have computer problems, and by acknowledging the user's frustration it becomes more likely that the client will see you as sympathetic.
Sometimes a problem legitimately can't be solved during the first support call. Maybe the fault is intermittent, or it requires some further diagnostics or research. If you can't provide an immediate answer to the customer's issue, make sure that you're taking him a step or two closer to an eventual solution. Begin a service record that documents the reported symptoms and your diagnostic efforts so far. Make sure that the next steps that should be taken -- by both you and the user -- are clear. Follow up with the client until the problem is rectified.
Finally, if you made a mistake during the repair, fix the problem at your cost. Don't charge the customer anything for resolving the error you made. HOWEVER, don't hesitate to educate the user if this complaint is actually a new unrelated issue. You're not obligated to fix for free a new problem that has only become apparent after the first was fixed.