Unfortunately, I don't think that this will be possible. If you are using a content editor web part, you need to click either the Apply or OK button in order to save the web part content. The original content editor web part exhibits the same behavior - In IE you have to press the OK button in the popup editor window and in Firefox you need to use the Apply or OK button in the tool pane.
We tried to workaround the problem on the client - e.g. always saving the content, including when you select "save and stop editing"). Unfortunately, SharePoint does not call the update function for the web part on the server, so the new content gets lost.
All the best,
the Telerik team