RSSOwl hasn't seen any updates in years. This results in some problems:

1. At least on Linux, there are major security bugs within RSSOwl. See Internal browser on Linux (XULRunner) has many known security issues #7 for details.
2. RSSOwl really needs to get ported to a more recent version of SWT and the Eclipse platform to support at least some of the now commonly used technologies such as touch devices, HiDPI displays and so on.
3. There are many known bugs. Just have a look at RSSOwl freezes when trying to open PDF files/links #6 or the forums for Discussion, Help or Developers.

How do we fix this? or do we discontinue RSSOwl?

Although I am a repository owner to RSSOwl I haven't used it in years any I won't have time to get anywhere near fixing RSSOwl myself. And I think it would be a good idea to stop developing and using RSSOwl in favor of one of the other >100 open source alternatives to RSSOwl.