I try to give you an answer from what a native speaker thinks. The two pronunciations have different meanings.
According to the dictionary, 着(zhao1) has the following definitions:
You can see the closest meaning is "2. 计策，办法 -- strategy, measure". Literally, 怎么着 means "how do you handle it?" when it is pronounced as zhao1.
By contrast, 着(zhe) has the following definitions:
It means '1. on-going', '2. pretty (+verb)', '3. emphasize the verb (imperative)', '4. introducing an object for an intransitive verb'.
None of the meanings is suitable for 怎么着 (how do you handle it?) However, it can mean 'how it is like.' For example, 你猜怎么着，我赢了一张免费票！Guess what (it is like), I got a free ticket. BTW, this phrase can also be pronounced as 怎么着(zhao1), because native speakers are not so strict about colloquial expressions, as long as it can be understood as the right mood and meaning.
At last, the phrase 怎么着 is mostly used in Northern China. In Southern China, a similar phrase 怎么样 or 怎么办 is often used. If you look at more examples, http://www.ichacha.net/%E4%BD%A0%E7%8C%9C%E6%80%8E%E4%B9%88%E7%9D%80.html, you may see yourself that it doesn't make sense to pronounce as zhe. :)