Transcript error, college unresponsive - how to handle?
A couple of suggestions. First, I think that having three "majors" is pretty rare, so a system error omitting the possibility would be easy to make. 

Second, I doubt that if you are good enough, then the third major isn't going to put you "over the line" in any application when two won't. (Caveat below)

Third, just explain it somewhere else in your application materials, such as your CV or cover letter, and also ask that the registrar will back you up if asked. Alternatively, have a faculty letter writer make it clear on your behalf. It is best if someone else, rather than yourself only, makes the statement so that it gains credibility. 

Caveat: If that third major is your specific field of interest in graduate school, then you may need to have a letter from the registrar as part of your materials. Though, if you are in the US, even that probably wouldn't be essential as it isn't an absolute requirement that you continue in grad school in the studies you did as an undergraduate. Other places are a bit more strict, perhaps.