So far, we have not detected any supersymmetric partners because they are heavier than the standard model particles. There are three possibilities for supersymmetric partners, they can either be less massive than standard model particles (and therefore there is a slight breaking in supersymmetry), the supersymmetric particles can be exactly the same mass as the standard model particles (and therefore there is no breaking in supersymmetry), or the supersymmetric particles could be more massive than the standard model particles (again, there is a slight breaking in supersymmetry). (5, 7, 8)
From models, it is clear that the supersymmetric partners are slightly more massive than the standard model particles. We know this because if there was not this slight breaking, the particles that supersymmetry predicts would not exist. Also, if they were the same mass as the standard model particles, we would have already observed them. If they were slightly less massive than the standard model particles, again, we would have already found them in the LHC for example. (5, 7, 8)
The fact that they are slightly larger proves to be a problem for detection because we need much more energy to create supersymmetric particles because they are more massive. Thus, we have not detected any supersymmetric particles in the LHC because we do not have enough energy to create such massive particles.If they were the same mass or less massive, we would have already predicted them, therefore, they must be slightly more massive and therefore, symmetry breaks. If we can build a much bigger particle accelerator, we can generate enough energy in order to create the supersymmetric particles. In the future if we can create a particle accelerator large enough to create supersymmetric particles, we will either have evidence that supersymmetry is real, or we will prove it is false. (5, 7, 8)