Sorry sometimes used the term for Virtual Machine,.. what you meant by the app getting down?, I see several links over the screenshot you take, I think is more a path issue, than tomcat issue.
Over your browser press F12 and see if you can find your css files clicking over the link from your page, if not start removing or adding until you find the css, could be happening with other parts from your HTML.
If the app were down from tomcat you will not see anything related with this app.
Thanks
-Mauro.