I've seen a few small businesses wrestle with this one. They start to grow, and management wants to start tracking project and admin activities for their financial reports. Technical staff usually view this as an intrusion into their work, not as a tool to save time in the long run. And many technical people don't like that PSA (or workflow package, or CRM, or whatever you may call it) is referred to as a way to "take intellect out of the job" (I swear that I've heard a BIG consulting company say this!).
PSA can be beneficial, as long as it's implemented properly, doesn't burden already over-worked IT staff, and shows real value to both practitioners and management alike. If none of these conditions are true, PSA will die quickly in the organization.