I'm very sorry for the inconvenience this causes! Do you have a search active in the sidebar when this happens? If so, we may know what's going on here; if you contact the support ninjas, they'll be able to help.
If you don't have a sidebar search active when this happens, The next time this happens, it would be quite helpful if you could send us the output of a "sample" command to the support ninjas, so the dev team on OmniOutliner can try to determine what the application is doing with all that CPU.
To take a sample report, you'll want to do the following:
1) Go to your Applications folder --> Utilities folder--> and launch "Activity Monitor".
2) A window will open that shows all the applications running on your machine. In the list, select our application.
3) Click on the "Inspect" button on the toolbar
4) Another window will pop-up. Click the "Sample" button on the lower left corner.
5) When it's done taking the sample, click the "Save..." button on the top right and email the document it creates
back to us. We'll have a look at it and figure out what's going on. Thanks very much!