These are not hard limitations, but values that can be found in real antennas.
One can make a patch antenna with air under it (so relative epsilon is 1). This results in a relative large patch size. One can make the patch larger, but this will cause other resonant modes and gives a complete other radiation pattern (with respect to the electrically half wave resonating patch).
The heigth (h) can be > 0.05 lambda, but then the antenna becomes thick. You know antennas must be small, otherwise there is no space for keyboard, display, batteries, etc... Heights above say 0.15 lambda will change the radiation pattern.
The heigth can also be less, but this results in very narrow bandwidth and increased loss (in fact it becomes a resonator instead of an antenna).
The physical length of the patch is strongly determined by the relative dielectric constant, high dielectric constant results in small patch size. Dielectric slows down the propagation velocity, so to get an electrically half wave patch, the physical length must be well below 0.5 lambda in case of substrates with high relative dielectric constant.