Hi albalex,
the reeds of each instrument react differently: if the gap between the reeds and the plate is too small, it’s difficult to play a strong staccato because the reeds don’t swing, and perhaps that’s the problem with your instrument. You could try not to blow too strong or you could try not to blow all the air directly into the mouthpiece but to release some air to the side (best blow on a “t” consonant or, for a more airy effect, a “tf”!), so you have a nice staccato sound and you can blow as strong as you want to.