This behaviour is due to the way SynthEdit 'sleeps' modules when they are not in use. When a note ends, the modules of that voice are stopped from processing until they are needed for a new note instance.
The disadvantage of this is that when you play a fresh note, there may be some audio in the signal path remaining from a previous note. This most affects modules with internal delay or feedback because they take some time to settle. Filters take longer to settle with high resonance settings.
There is no universal fix unfortunately, but placing a VCA (controlled by an envelope) after the filter can help mask the effect because the VCA will take a short time to 'Attack' to full volume. This hides the click.
Also avoid using high resonance if possible, or reduce it. For best results you may need to experiment with different 'Attack' settings.