Why are they so rare?
White lions are a result of leucism, or lack of pigment which results in light coat and eyes. In lions, leucism is caused by getting a copy of a gene which has a recessive mutation from both mom and dad. For two tawny lions (the typical brown/tan color) to have a white lion cub, both lions would have to be carriers of the recessive allele, meaning they have the recessive copy but they display the dominant one.
Where did all the white lions go for 13 years?
If we think of this as a simple Mendelian trait, when a carrier mates with a carrier they have a 25% chance of creating a white cub and a 50% chance of creating more carriers. When a carrier mates with a full tawny they have a 50% chance of carriers. So, for 13 years, the recessive allele was 'hiding.' Because the white lion didn't disappear completely, this means that the carriers either weren't breeding with other carriers or when they did, neither of them passed along the recessive allele to the same cub (the other 75%).
It is quite possible that the statistics are way more complicated and that there may even be more than one way to be 'white.' It has been speculated that light coat in white lions with yellow eyes may we caused by a different gene than in white lions with blue eyes (the TYR gene versus a gene similar to what creates white cats and white tigers). Genomic analysis of big cats is just beginning but don't you worry, we're getting to the bottom of it!