
This time specifically on the "natural born citizen" clause, claiming since his father was not a US citizen he does not qualify. Natural born citizen is a specific subclass of citizen, requiring born on US soil to two US citizen parents they claim. Apparently they have an old Supreme Court decision and historical documents backing up their story, or so they say.
Now these issues have gone around court a few times, but the merit of the claims were never ruled on. Lack of standing and too late were the common answers. The last Court ruling was "after inauguration it is too late". But with a reelection coming up it can all come back up again. People in all fifty States could conceivable sue their State AG over this issue for both primary and general election in addition to a Federal case.
A particularly heavy Republican State could try and make life miserable for Obama. They could rule that Obama does not qualify as States are responsible for vetting candidates and remove him from the ballot forcing an obvious Federal law suit.