We are not making enhancements to PI System Tray, as we are working on a more Enterprise-Wide view of health, and support of PI System Manageability. This is the type of health status we would like to surface in an upcoming version of the health tool.
Having said that, if you have specific use case around failed analyses, and what you would like to see/be notified on, please let us know (and submit this under the category of PI System Health.)