The most common type of dwarfism in rabbits is achondroplasia, which is lethal in most cases if the rabbit is homozygous (2 dwarf genes). Achondroplasia is also the most common form of dwarfism in humans (also usually homozygous lethal). However, in rare cases, the homozygous may survive, but with a significantly shorter lifespan. There are a couple cases of homozygous humans surviving until about the age of 2.
There are 100's of known forms of dwarfism, and not all are homozygous lethal.
In rabbits, the achondroplasia dwarf is born of normal size, but rapidly deteriorates and dies within about 3 days. They generally have a dome-shape head and hind limbs showing atrophy within a day or two.