The issue is with the passenger side running light that keeps going bad. Well, the bulb itself is good but one of the contacts on the bulb which is like a blob of solder or something like that keeps getting so hot that it melts one of the sides enough so the light bulb contact doesn't. The problem is pervasive enough that I have to keep replacing the light bulb after about a week. I'm thinking of replacing the socket P/N 68685062AA but it is doubtful that is the problem. Any other ideas?

Having lights burn out within the first six months of owning a vehicle is completely unacceptable to me. I have NEVER had this many issues with any vehicle I have ever owned with less than 60,000 miles on it. I have not replaced them because those lights do not count in an inspection.