Are they all one page per visit? Are they all visiting a different page each time?
It's been several years, but I had something like this happen to me. Had 50+ visits all coming from the same city, all direct traffic, all with a single page per visit. I happened to have another analytics package on the site at the time, and saw that it was the same IP and actually one user visiting 50+ pages. For some reason, GA though they were different people.
If you look at some of the technology reports in GA, you might look to see if they have the exact same browser resolution, flash version, etc. That may help indicate if it's actually one computer that has some settings that are making GA think it is separate visits.