With other cases still pending, however, alternative routes may eventually lead to reform of the NSA’s habits on some level. Lower courts are still in the midst of deciding what action they will take with regards to similar lawsuits filed by other groups in response to the Snowden leaks and the revelations they made possible. The American Civil Liberties Union, the Electronic Frontier Foundation and conservative legal activist Larry Klayman have filed separate civil lawsuits in various US District Courts challenging the NSA’s program, all of which are still pending.
That is almost certainly the practical reason why the Supreme Court has denied EPIC's petition for a writ of mandamus - they would prefer to wait for these various lower courts to hear these cases, do their research, and issue their opinions. Essentially, EPIC was leap frogging most of the judicial structure to get a hearing on the matter before the lower courts have had enough time to hear enough of the other cases and to start issuing opinions that do the basic legwork for the Supreme Court.