Your super zoom camera has an equivalent zoom to a (non-existent) 960mm telephoto lens on a DSLR. That is incredibly long. A long telephoto lens greatly increases the effect of hand held camera shake, like distance increases your hand shakes when holding a laser pointer. At 2 feet you can hold the laser pointer's red dot totally still. At 200 feet the dot will be jumping around like you had the shakes.
You need faster shutter speed to eliminate the hand shakes as you zoom in farther and farther. Without Image Stabilization, the rule of thumb is a shutter speed that is the reciprocal of the lens length in mm's. So a 60mm lens needs a shutter speed of 1/60th of a second or faster. A 200mm lens needs a 1/200th of a second or faster shutter, etc., so your 960mm equivalent lens would need a really fast 1/1000th of a second shutter or faster to counter hand shake. And that assumes your technique is very good.
The image stabilizer can compensate and allow for a slower shutter but keep in mind what it is having to overcome. At that distance you have to be holding it pretty still or the IS won't stand a chance. If you are fully zoomed you should consider setting the shutter speed yourself, using Tv (shutter priority) mode. That will keep the camera from setting a shutter that is too slow, which it often will do if you leave it on Auto mode. I would set it to 1/500th or faster if you are getting blurry shots. If that is still blurry try faster.
You may also benefit from using a monopod. Basically just a collapsible stick with a camera mount on top. You therefore carry a solid brace with you, and you can hold the camera a lot more stable than you could with your hands.
Scott
Canon 5d mk 4, Canon 6D, EF 70-200mm L f/2.8 IS mk2; EF 16-35 f/2.8 L mk. III; Sigma 35mm f/1.4 "Art" EF 100mm f/2.8L Macro; EF 85mm f/1.8; EF 1.4x extender mk. 3; EF 24-105 f/4 L; EF-S 17-55mm f/2.8 IS; 3x Phottix Mitros+ speedlites
Why do so many people say "FER-tographer"? Do they take "fertographs"?