Yeah thats what I was going to say, check your horn maybe some kind of mechanical problem, when you press down those pedals or levers, at some point they come in contact with the body of the horn and sometimes the small piece of cork that is on the other end of the pedal falls off small leak happens. Or get a old reed that you know you can hit those notes with and try it .

playing altissimo is a bit like singing.
if you opened your mouth wide and sang “La” for 10 seconds with out moving your jaw and at the same raising and lowering the pitch without moving your jaw. Then you learn to control changing the pitch at the back of the tongue/mouth. Don’t change the pitch at the front of your mouth by moving your jaw like in chewing and biting.

then next just blow on the mouthpiece with a reed, but not connected to the sax neck. To get like playing altissimo, now raise and lower the pitches on the mouthpiece using the back of the tongue/mouthpiece just like in the singing exercise. don’t change pitch by varying lip pressure.

Then start playing overtone exercises in JF’s book. the 1st three overtones and the last 3 upper overtones are the easiest to master.
if you cant get an overtone, try a higher one – master that and go down to a lower overtone.

The best overtone building exercise is to slur up and down through the different overtones like in the singing exercise. When you have learnt to play an overtone, you must practice slurring between the overtone note and the actual keyed note repeatedly – it takes a lot of breath control – this will build up your altissimo muscles.

You can also have a go at the various altissimo notes while learning overtones, you will find that some altissimo notes are easier than others just like any other notes on the sax.

Yes, so without being there it’s always a guessing game so the first thing is to make sure your sax is working properly otherwise it’ll never get better no matter how hard you try!
The other member’s suggestions are good as well.
my only other suggestion is to look at the video on my blog about playing those high notes which sound too thin and out of tune.
it’s one of the more recent videos there so you should find it easily. but check it out because it deals with this exact problem, which is common by the way and why I recorded a video on it!