Context. Titan's stratosphere contains oxygen compounds (CO, CO 2 , and H 2 O), implying an external source of oxygen whose nature is still uncertain. Recent observations from the Herschel Space Observatory using the HIFI and PACS instruments and the Cassini/CIRS, as well as steady-state photochemical modeling indicate that the amounts of CO 2 and H 2 O in Titan's stratosphere may imply inconsistent values of the OH/H 2 O input flux, and that the oxygen source is time-variable. Aims. We attempt to reconcile the H 2 O and CO 2 observed profiles in Titan's atmosphere by using an updated photochemical scheme and developing several time-dependent scenarios for the influx/evolution of oxygen species. Methods. We use a time-dependent photochemical model of Titan's atmosphere to calculate effective lifetimes and the response of Titan's oxygen compounds to changes in the oxygen input flux. Two variants for the C-H-O chemical network are considered. We investigate a time-variable Enceladus source and the evolution of material delivered by a cometary impact. Results. We find that the effective lifetime of H 2 O in Titan's atmosphere is only a factor of six shorter than that of CO 2 and exceeds 10 yr below 200 km. A time-variable Enceladus source, involving a decrease by a factor of 5-20 in the OH/H 2 O flux over the last few centuries, shows promise in explaining the relative CO 2 /H 2 O profiles. However, if the previous measurements from the Herschel Space Observatory are representative of Titan's atmospheric water, an additional H 2 O loss to the haze term is needed to bring the model in full agreement with the data. In an alternate situation, CO 2 production following a cometary impact that occurred at least 220-300 yr ago can in principle explain the CO 2 "excess" in Titan's stratosphere, but this scenario is highly unlikely, given the estimates of the impact rate at Titan.