I would ask your sensei or some of the senior students for suggestions if this is an exercise that's done at your dojo. There might be someone who went through the same difficulty when learning it, or they may be able to help you find alternate exercises that build the same skills that this exercise is intended to build.
FWIW, I suspect a lot of people who can take very good falls in real practice with a partner can't jump 4 feet in the air. It seems like a very different skill (falling vs jumping). I might get some clarification from your teacher if they actually consider this jumping to be very important for its own sake or if it's just a way to get some height so you can practice controlling your body in space all the way through a fall, or a way to build core strength, or some other thing. Also I don't know how wide a sparring pad is but it might be you're supposed to drop yourself over it rather than jumping over it.
Again, someone from your dojo who knows the exercise and what it's for and how other people have learned it is a good person to ask. Don't be too shy or intimidated by them