Sounds like the slit might be a little tight right at the tip and with pressure flexes open so the ink can flow. I presume that you have cleaned the feed and nib.
Here is a pretty good article on nib adjustment http://www.nibs.com/Article6.html
If the pen is valuable, you might want to take it to a Dallas Pen Club meeting. As a pen maker, I want to be able to do a decent adjustment myself, so one of the inexpensive kit nibs would be good to learn on.