Any equipment installed into a house that has served more than ten years may have to be replaced, not only because they are not working but because they consume more electricity and thus cost you more in the long run. Air conditioning, central heating elements and many other systems that are installed into a home need constant monitoring and maintenance or else they risk breaking down in the most unexpected times. Newer models also have the advantage of the inclusion of newer more energy efficient parts that saves you money in the long run.
The older the appliance the lower the safety of such older equipment due to normal wear and tear that it goes through every time you use it. The old reliable one might still have some life to it but try to look out of the box and visualize the overall efficiency of your AC for example and compare it to newer models, they might cost you now, but would surely save you more in the future.