I have a Park PFP-4 pump with a dual head that had the same problem, it developed an intermittent leak through the Schrader side when I tried to inflate a presta valve.
When I took it apart I found the head contains a rubber ball about 1/4" in diameter that is positioned between the two valve holes and acts as a check valve. When you push a presta valve into its opening the stem is supposed to push the ball toward the Schrader side and block that opening and vise-versa. It didn't always seal but cleaning the ball and the ball seats pretty much ended the problem.
Actually what really ended the problem for good was substituting a Hirame presta-only valve head for the OEM one but that's another topic all in itself.
