when "住" is used as a suffix of a verb. It has two possible meanings:
- To express that something would be secured, under your control.
- To express that the motion stops, or pauses, to be stationary.
In your case, “住" is used with the second meaning.We have words "愣住","呆住","怔住",etc..They mean the same: [someone] gets surprised, or astonished, or bewildered [so he stops other actions and just stay there like a statue].
"着" is a word to show the progress tense, that the action of the verb is going on.You could say "他一直在那儿愣着(He is standing there all the time)",but "着" doesn't show the transformation between "to be in action" and "stop to be stationary".
I also want to show you an example for the first meaning. Imagine that you are a policeman, and your boss asks you to moniter a suspect.You boss would say,
你的任务就是看(kān)住他。 Your task is to watch over him[make sure he won't escape]. Here "住" shows that your boss requires you to keep him in your sight securely.
Unfortunately, the suspect escaped. You report this to your boss:
我一整天都在 看着 他，但还是没 看住。 I was wathing over him all the day, but I still failed.