And what is happening when you try to kill it? Do you get a message box? Or does the process just not disappear?
There are some background processes which use a "guardian process" (or the program's front-end) that will restart the background process immediately after it is terminated, such as certain viruses, google updater, or zunebusenum for Microsoft's Zune. I personally find this behavior to be completely unacceptable under any situation on a personal computer at any time ever. If a user tries to terminate a process, it must end. Who's in charge of who?
It might seem benign in certain cases, but it undermines a users authority over his own machine. I will go to any length to stop a process that I don't want running.
It might seem appropriate to ensure that certain processes are running, say, on an employees computer, but I completely disagree. If there is a process that must be running on an employees computer, the process should phone home so that the main office knows that it is running, and it should have an obvious presence on the computer. If you need to outsmart employees, you're in a worse situation than you realize.
So who is going to be using your software?