Offer hosting
Of course, this model can only be used if the project is hostable in some way. Examples are sentry and the paid hosting option at wordpress.com
A secondary problem: running/maintaining a hosted version of a product can be a distraction, depending on how heavy the support load is. If you're really lucky, you can just set the code running and forget it; if it's more complex, though, handling support queries can easily consume a full time resource (speaking from my experience running a SaaS company).
This works nicely for "ready to use" open-source apps (like sentry indeed), less for components or frameworks like Sidekiq or my own Kiba ETL, which are building blocks that you can use.
I second @freakboy3742 too, also running a SaaS, that support can be an issue depending on who you target, and how complex is your app!
Another secondary problem: You have to be available all the time. If your service is down, you have to bring it up immediately.
Sidenote: I believe this is how ghost operates.
I'd call the bit that @jayfk mentioned the primary problem. Being "on call" and responsible for uptime for a hosted service is a sure-fire way to burn yourself out.