ps -aux | grep "app name"
I believe as you say there's a chance the new version will fix it, but I prefer to manage all installed packages via pkg.I'm a long time x11/tint user in OpenBSD and Linux and have not experienced persistent display of closed apps in the panel. I do use it with OpenBox.
Typically, if you go to the developers, the first thing you'll be asked is if you are running the latest version.