My Air Conditioning has problems keeping up with keeping the house at my temp of 76 when its 110 outside.?

It only happens when the outside temp reaches 110. I live in phoenix so that happens on several days around here. Going to hit at least 116 today. I am wondering if that is normal, my house never goes about 84 but that is still warm for me. Once the temp drops below 105 my AC is able to get me back to 76 degrees in a couple of hours. I have already had someone out last month for another problem. I would really hate to have to call them back out for a normal thing. Looking at some websites it says the home AC is only usually good to drop the inside temp by 15-20 degrees from the outside temp. Appreciate any feedback.