It took me a while to figure out what was happening, but now I have it nailed down. Precognition will go on cooldown if you don't have enough psi for it at the end of the turn. That's how it's supposed to work. How it actually works is it will drain however much psi it needs, THEN if you have less than it needs after that, it will go on cooldown.
For example, let's say it costs 20 psi per turn. You have 25 psi points left with precognition active. You end your turn, it drains 20, you now have 5 left, and it goes on cooldown because you have less than 20 left AFTER it drained the 20. So you would need at least 40 before ending your turn to keep it going.