I bet if you were to graph this out, I bet 10% of the guys have 90% of the fatigue calls. That
Pareto distribution things strikes again, you could probably even do more crazy math to identify potential freeloaders and mooches - don't do this it's a waste of your life. You're seldom going to get pilots to admit that there are other pilots who abuse the sick-call/fatigue/whatever system. Probably because most people have worked for such terrible places that we don't want to risk any reduction in the ability to drop trips/call in/whatever when we feel crappy. Also, admitting that some people who are pilots are kind of sucky freeloaders feels like betrayal.
Still, some people kind of suck - that's just how it's going to be. Also, chances are that even the guys who kind of suck will use a system like a fatigue call system how it's supposed to occasionally, so even if they are sucky, the system is still serving it's purpose. I would look at this not like it's something that is going to "hurt" the company if it's abused, but as something that is a sort of insurance to keep sleepy pilots out from behind the yoke. Change your mindset if you can.
A no-fault fatigue call system is a money saver in the long run if it prevents even one airplane from being flown into a mountain. In the short run, keeping sleepy pilots out of the cockpit is insurance that keeps the FAA from calling your office (you're a DO, right? Do you want to explain to your POI why Chronically-Tired Terry decided to turn the wrong way on the departure?). Finally, don't think about it like you're losing anything - you're not losing anything by pilots fatigue calling erroneously if occasionally - you're actually getting over on the fake-fatigue caller guys. Lemme explain.
See, those guys who really abuse the system often times think they're smarter than everyone else. They're usually not, but I digress. They think they're so clever when they plan a vacation and fatigue call before coming back on or something like that. "Hah, I got an extra day of paid vacation, chumps!" If you can tolerate the guy in the rest of the operation, then that "victory" where he got over on you is a major benefit to the guy and really strokes his ego. If you can't tolerate that guy, think, "well, I just paid a few hundred dollars to not have to deal with that dumbass until he's back on shift." Either way, it's a benefit. This is now a pilot that is less likely to be looking for a job. Conversely, if the guy uses a fatigue call to go to a job interview and gets the job, well, then he's someone else's problem.
Regardless, look on the fatigue call system as insurance against the FAA for your own sanity and as a benefit to your pilots. I would consider it a sunk cost and move on. When it comes to the individual people and the personal interactions that get irritating when you're pretty sure that a pilot is trying to get over on you, don't look at it like "he got over on me" - look at it like, "heh, that guy thinks he's so smart and thinks he's playing me, meanwhile he's not out trying to find a job and his ass is back in the schedule on Monday." Regardless, if you can re-frame the problem it might help any irritation that comes up. At least that's the sort of thing I do when I deal with irritating people in the workplace.
If you begin to suspect that some percentage of your staff are freeloading asshats in excess of 10-20% (that is to say fatigue calls are not Pareto Distributed), it stands to reason that you need to change how you're hiring because you are probably • up. In that case, the problem really lies in hiring in my opinion and you've gotta figure out a strategy to identify potential free-loaders before they enter the organization, but as long as there aren't seemingly abnormal fatigue calls from greater than 10-20% of the crewmembers, I'd chock it up to the typical distribution of human foolishness, consider it a sunk cost, and move on.
This is another topic, is this place calling sick time "PTO"? Because that's a whole other thing I could bust a blood vessel about. It's either sick time or it's PTO.
Not that it's an airline, but where I work now, PTO all comes from the same bank - it's kind of awesome actually now that I work from home. My wife's PTO at the hospital works the same, but when she's sick she has the option to use PTO or just take the day off without pay. At Big Fortune 50 Inc we had a system for PTO for the pilots that was effectively outside the normal HR system,
and had earned PTO and sick pay.
Different sorts of organizations work in wildly different ways, I wouldn't get worked up about it.