What causes a treasure Yeti to run away?

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.

Just get double sunflowers and keep some sun in the bank. As soon as he appears, plant a coconut cannon and blast him. I think that drops him completely or he only needs a couple more pea shots. I've killed two this way.