First, we must understand that before limbless snakes, there was an ancestor that possessed limbs. In the population of this ancestor, a mutation occurred in one of the individuals that caused it not to develop limbs.
Currently, the data suggest that the loss of limbs was due to the Sonic hedgehog gene and the regulatory region of this gene, the ZRS region.
The mutation (a deletion or loss of nucleotides) in the regulatory region (ZRS) meant that the sonic hedgehog gene could not be expressed correctly and therefore the gene could not drive limb development.
We already know how the loss of limbs occurred, now the question is, how was this feature maintained over time?
Today, snakes do not have limbs because the limbless ancestor was able to reproduce in a great way and therefore its descendants have lasted until today. This was probably because the lack of limbs gave it an advantage and a greater survival compared to the other animals in the population that did have limbs.