how to judge a program is dead

how to judge a program is dead

I am new begginer on winodws programming, I am Writing a Service System
which should be running 7*24h on windows. But when I test the system,I
found some problem that not happen usually, I have test this program so
many times, this phenomenon only happened one or two time which as follow
description: The Service system did not work in fact,or I think it has
been deadlock, but when I open the Task Manager, the Process of that
Service system is still there. Because this phenomenon is not happened so
frequently, I cannot find where the bug, But I want to know is
how can I know a process is not working now though it have a process id in
the task manager?
What could lead to this phenomenon except the deadlock caused by
Multithreading's wrong Mutex lock behaivor?