Sorry to tell you, with suckers you just have to keep lopping them off. I've read that if you follow the suckers' root all the way back to the original plant and cut it off there, your results may last longer, but I have not tried this myself.
But what a labor of love. Mine are about 9 feet tall and I have them the entire length of my yard. Birds nesting in there too taking care of some of the garden insects. I love my forsythia. It also doubles as our WIFFLE BALL fence. Boy, you can lose some balls in there too. No problem though, they turn up in the Fall. ha ha.