Master numbers are, structurally, nothing more than the double-digit numbers made of a single repeated digit — 11, 22, and 33 are the ones that survive into adulthood in most systems, while 44, 55, and beyond generally don't get the same treatment.
The reasoning offered by numerology writers is more aesthetic than mathematical: 11 is seen as a kind of amplified 2, carrying the same underlying theme (partnership, sensitivity, harmony) but at a pitch loud enough that reducing it further is thought to lose something.
This is a convention, not a computational necessity — a Vedic-style practitioner who reduces every total fully would read the same name's vowel sum simply as a 2, with none of the "master" framing attached.
