The gas mass of protoplanetary disks, and the gas-to-dust ratio, are two key elements driving the evolution of these disks and the formation of planetary system. We explore here to what extent CO (or its isotopologues) can be used as a tracer of gas mass. We use a detailed gas-grain chemical model and study the evolution of the disk composition, starting from a dense pre-stellar core composition. We explore a range of disk temperature profiles, cosmic rays ionization rates, and disk ages for a disk model representative of T Tauri stars. At the high densities that prevail in disks, we find that, due to fast reactions on grain surfaces, CO can be converted to less volatile forms (principally s-CO$_2$, and to a lesser extent s-CH$_4$) instead of being evaporated over a wide range of temperature. The canonical gas-phase abundance of 10$^{-4}$ is only reached above about 30-35 K. The dominant Carbon bearing entity depends on the temperature structure and age of the disk. The chemical evolution of CO is also sensitive to the cosmic rays ionization rate. Larger gas phase CO abundances are found in younger disks. Initial conditions, such as parent cloud age and density, have a limited impact. This study reveals that CO gas-phase abundance is heavily dependent on grain surface processes, which remain very incompletely understood so far. The strong dependence on dust temperature profile makes CO a poor tracer of the gas-phase content of disks.