Today I downloaded the EA Fifa app on my iPad and used Game Center for it. I then opened my NBA Mobile Live app and it my lost account appeared under the Game Center account option (probably since I signed into Game Center on Fifa)! I guess since I rarely ever select which account I'm using for NBA Mobile Live, I didn't realize it was through Game Center. Although I'm not sure why I was logged out from it to begin with.
One thing I realized though is that my profile on the EA website and my Game Center profile on my iPad/iPhone have absolutely nothing to do with each other, except a shared email address. So when I sent in an issue through the EA site about my NBA Mobile Live problem and spoke to the support member on the phone, I'm not sure what account they were looking at and commenting on, but it wasn't one connected to my iPad.
How would I have even been able to send in an issue about my account on my iPad, using the EA website, if that account only exists on the NBA Mobile Live app (an account either through Game Center or as a Guest)?