Which fatalities are you trying to perform? If you have to press up at some point in the combination, then you do need to hold block, but otherwise, no, it's not a prerequisite. It depends where you're getting your fatality list from, but more often than not, they'll tell you when you need to hold block.
It's a bit difficult to offer you help when we don't know exactly what you're doing, but if your character is jumping instead of doing the fatality, and you're not required to press up, then you're obviously hitting a diagonal by accident (like forward+up instead of just forward). If you are required to press up, then you need to hold block, like I said, but also keep in mind that you have to let go of it before you hit the action button (high punch, low punch, etc.).
Another tip I can offer is that when you hit the action button is very crucial. There should be a slight delay between the last direction you tap and the action button. Let me offer an example of both of these in the same fatality...
Ermac's Telekinetic Slam (down, up, down, down, down, block): From about sweep distance, hold block, then tap down, up, down, down, down, making sure to release block some time after you press up, but before the action button is hit, which is block in this case (which may be confusing, but in this example it will help to make sure you release block initially). After you tap down for the last time, hit block again (don't hold it). Remember, there's a delay here, and my guess is, if you can't pull off this particular fatality, it's because you're either not allowing enough of a delay (like you're hitting down and block simultaneously) or you're allowing too much of a delay.