The problem is... you're on the wrong side of the equator. The Coriolis Force and geomagnetic anomolies are the culprits.[8D]

Really though, any of the several possibilities that have been mentioned can cause your problem. Even your basic shooting stance can be causing the sight pins to be misaligned.

First thing I'd suggest looking at is your grip. Extend your bow arm to the side with your hand flat, thumb extended to the side and palm down. Rotate your shoulder so that the inside bend of your elbow is 90 degrees from the floor. If needed, rotate your forearm to bring the palm back flat and parallel with the floor. Now, curl the small, ring and middle fingers into the palm of your hand and relax the entire hand while keeping the wrist straight. Now, keeping the inside bend of your elbow perpendicular to the floor, rotate your forearm so that your thumb is pointing up at 45 degrees.

That is your grip position when shooting the bow. The bow sits in the pocket between the the index finger and thumb, and just on the inside part of the meat of the palm. The index finger is relaxed and naturally curled around the front of the grip, possibly touching the thumb. The other fingers are curled (but relaxed) between the grip and the palm.

(When you get the basic feel of the grip, it will no longer be necessary to curl the other three fingers between the grip and the palm. But until the grip is ingrained in your muscle memory, I suggest you keep them there.)

That style grip allows you to hold the bow with minimal hand contact and torque. It also allows the bow to suspend itself straight up and down, eliminating cant. Rotating the elbow vertical with the floor gets the meat of the forearm out of the string's way so you won't be raking chunks of hide off your arm every time you shoot - or, at least, having the string bounce off your arm and changing your arrow's flight path.

Most people say to use a wrist sling and keep the grip totally loose. I do not subscribe to that idea. I hold enough tension in my index finger (which is naturally curled around the front of the grip. Remember?) to keep the bow in my hand when I shoot. There are a thousand and one different ways to grip a bow. Of course, I think my way is best.

Once you get your grip squared away, you can begin making sure you don't have any mechanical issues with the bow/arrow combination itself. I thorougly expect you'll need to retune your centershot setting for your rest.