Without knowing what the app/service is I can't really say if it's behaving appropriately, but we need to be clear on how Android reports and manages memory.
Android reports any app that is stored in active memory as running, but it isn't necessarily impacting your phone in terms of performance or power consumption. Android tries to place as much in active memory as possible because unused memory is a waste of resources in a compact mobile OS. Once you've used an app, it will continue to show as running because it remains cached in its last used state so that if you use it again it launches faster and picks up where you left off. For the most part, however, there is no process running until you do use it again.
Trying to manage your own memory is counterproductive. You will not only become frustrated with Android trying to fill unused memory, the constant starting and stopping of services will have a greater negative impact on your device. If it's better battery life and faster performance you are looking for we can suggest other, better ways to achieve this.
To confirm this, go to menu>settings>apps and click on the "running" tab. There you can toggle between cached processes and running processes. Those listed as cached are really just sitting there doing nothing. If the app in question is listed there, forget about it. If it is listed as running, it may be providing a necessary service to some other app.
Let us know what it is and we can figure it out.
