Because the network suits watched the first episode of Season 3, Spock’s Brain and said, you got to be kidding me!
Spock had two lobotomies in 24 hours without a single hair moved on his head!
Edit: According to one of the commenters, lobotomies are done through the eyehole and not the skull, so it makes the “2 lobotomies” joke anatomically and surgically incorrect, and therefore not funny. I humbly submit for his (and yours, dear readers) approval the following revision:
Spock had two craniotomies in 24 hours without a single hair moved on his head!
It also featured lines like this:
And this:
and of course, most famously
The real reason is NBC kept cutting the budgets, then they moved the show to Friday night, when no one watches… they really never gave the 3rd season a shot.