A stomach cell dies after 2 days, will this short life span, mean that even in our own life span our stomache cells will evolute to become stronger?

Well probably not in the way you are thinking. The cells that form the surface of the gut don't themselves reproduce, but are replaced from underlying stem cells (although there are usually intermediate generations). Because the surface cells aren't replicating, there wouldn't be any multiplication of the number of mutant cells. They would hang around for a while longer, then die. The stem cells could have some mutation that resulted in progeny cells better equiped to surviving the stomach. However, the stem cells would still be under the same controls that regulate the production of progeny, so they wouldn't produce any more than usual.

 

If a cell were to mutate in such a way as to escape the controls placed on its replication, then it would be at a competitive advantage with surrounding cells. This is one of the stages in the formation of cancer, which can be viewed as an evolutionary process.

so is stomache cancer quite comman as a aresult?

Maybe, I don't know that much about cancer. However, there is a strong correlation between the incidence of stomach cancer and diet, as well with infection with the bacterium Helicobacter pylori. I would guess that stomach cancer is fairly common because the stomach constantly being exposed to foreign carcinogens.