If you stay several days, your kidneys will re-balance the pH of the blood, resetting your system to your new environment. If you were to continue even higher, your body would compensate and re-balance again. Ultimately, you would reach the limit of your body's ability to compensate. This ability of your body to adapt to altitude and the speed with which it happens vary widely from person to person. They appear to have no relationship to physical fitness or gender.
Some people adapt to altitude better than others.
However, everyone's ability to adapt to higher altitudes is reduced by dehydration, alcohol and other depressants, and overexertion. The best way to adapt to higher altitude is to take your time, maintain hydration, stay away from depressants, and take it easy. Allow your normal compensatory mechanisms the time necessary to work by ascending in stages. Climb no faster than your body can adapt. Do not overexert on the first day at the new altitude, and plan to remain for two to three days before proceeding higher.