We just don't have a good enough model. Once (if) a good mathematical model that takes into account enough information is created, then the 'deep' mathematics that you speak of would once again be successful in predicting things.
Economic 'explanations' exist to privilege certain actors through pseudo-rational justifications for personal benefit, not to predict economic reality.
If you look objectively at economic models, you'll see that all the mainstream models are uniformly hopeless at predicting the future, and some of the most highly placed analysts have absolutely no insight into future events - not just in defiance of theory, but often in defiance of simple common sense.
See e.g.
http://www.bbc.co.uk/news/business-30699476
This is characteristic of a pseudoscience, not a real science.
The only way to profit from this is to buy government policy and to fix the markets - something the bigger players are well aware of, and have been doing enthusiastically for decades now.
I'm basing this on having tried to find it myself, and becoming convinced that there is no such theory, and also that the rest of the field is correct in not trying to find such a theory.
Any viable model of the economy would therefore have to recursively contain a model of the model of the economy and so on.
> As soon as you implement the results of your sufficiently-sophisticated model, the economy will start to be influenced by that.
This is called a feedback loop, systems with feedback loops are well understood.