I'm not sure if it satisfies the criteria of "a long time with little progress", but one example of a simultaneous mathematical discovery is the discovery of the hook length formula. Here is how Bruce Sagan describes it in his book The Symmetric Group:

One Thursday in May of 1953, Robinson was visiting Frame at Michigan State University. Discussing the work of Staal (a student of Robinson), Frame was led to conjecture the hook formula. At first Robinson could not believe that such a simple formula existed, but after trying some examples he became convinced, and together they proved the identity. On Saturday they went to the University of Michigan, where Frame presented their new result after a lecture by Robinson. This surprised Thrall, who was in the audience, because he had just proved the same result on the same day!