Why doesn't crossing over happen in mitosis?
It can actually on very rare occasions however, it is also highly problematic and generally creates deleterious mutations and can inactivate genes. Depending on the location of the cell and the cross-over within the genome, it can also contribute to the formation of cancer. For instance, in the case of retinoblastoma, if there is one mutated copy of RAS on one chromosome and a normal copy on the other and mitotic crossing over occurs, then you can potentially remove the protective nonmutant copy of RAS from one of the daughter cells. This cell is then one step closer to becoming tumorgenic. 

Thus, one reason this may not occur ordinarily is to reduce the chance of causing such a cancer. As for why it does occur on the rare times it does, I am not certain as of the time of writing this.

Reference: The Biology of Cancer, by Robert A. Weinberg