Mr. Clinton himself was a Democratic-Republican, and had even been offered his uncle George Clinton's place on the Madison ticket due to his uncle's failing health. As such, many Federalists may have felt they were being required to choose between two members of the same party. At the same time Clinton's running mate, Jared Ingersoll, was a diehard Federalist, which likely alienated a lot of Democratic-Republican voters.
In short, many Federalists likely saw him as still a Democratic-Republican, and many Democratic-Republicans likely saw him as a traitor, and so in both cases would not support him.