Block persistent notifications, but keep regular ones?

I use Steam and Skype. I'd like to be able to hide the ongoing "Online" notifications each service have without them being killed in the background. Skype has an option to disable the ongoing notification, but then I have a ton of trouble with it randomly being killed. I don't want to completely block notifications because then I won't get notifications when I get messages.

I'm running Lollipop. I can root if there's a solution that uses that.