Just checked the wiki, but it doesn't say anything about the time when will it run away. But it's one of his specialties, so you have to kill him ASAP. Quote from there:
Zombie Yeti
A rare and curious creature.
Toughness: high
Special: runs away after a short while
Little is known about the Zombie Yeti other than his name, birth date,
social security number, educational history, past work experience, and
sandwich preference (roast beef and Swiss).
So it seems that running away is his normal behavior.
The wiki also provides a bit of strategy against them:
Just do whatever you do to kill Buckethead Zombies (obviously besides
using Magnet-shrooms). If it tries to run away, it can be stopped by
planting a Wall-nut or another defensive plant in its path such as the
Pumpkin or Tall-nut.
...
or an instant kill like Jalapeno, Squash or Cherry Bomb can be used.
It also says that it can take only 46 normal damage shots, so a Plant Food planted on a Repeater should be enough to take him down I guess.
EDIT
Apparently there is also a Treasure Yeti, a new zombie in PvZ2. Probably it's the one that you encountered.
Not much is said about him, but:
Toughness: Dense
Speed: Basic
Special: Runs away after a short while, drops a lunchbox if killed
But comparing some other zombies(Zombie, Conehead Zombie and Buckethead Zombie) it looks like they still take the exact same amount of damage, so I'd assume that the Yeti will be as tough as in the first game(I've never seen him though).
EDIT 2
Yes, he runs away after some time and not distance. Just planted a walnut right in front of him and after a short while he flew away like a little scared girl.
Best Answer
The Yeti is not gone from the game; he is however much more rare.
The Yeti now appears once every couple weeks. Prior to the Modern Day update, I'd get him once about every 18 hours.