Below is my steps to find this issue:

1. Open the browser with IE 10 mode or genuine IE10.
2. Create a table with Editor.
3. Right click the table and then select table properties. Then click Table Layouts tab and select a style.
4. Click OK, the style can be kept this moment in Design tab.
5. Click HTML tab and find the CSS details are missing and click Design tab again, the style cannot be kept.
6. There is no reproduces with chrome or IE 11. 
7. I also test this case from your ow site https://demos.telerik.com/aspnet-ajax/editor/examples/overview/defaultcs.aspx


A video repro is also attached