I have a class that needs to run 24x7. It uses a Timers.Timer to execute an elapsed event in a calculated interval. After some time, 3-5 days, the timer just stops executing
Your threads have a problem. An explanation of what the specific counters mean.
There should not be ~800 threads in your application(!). Furthermore they seem to be unable to completely start (for some reason). It could be resource exhaustion (probably memory). Heavy paging.
Find out why there are so many threads. Maybe you are running lots of blocking work on many threads or posting many such work items to the threadpool.