The ac losses of NbTi multifilamentary superconducting wires with a copper matrix were measured using a sensitive calorimetric method. The wire samples, which have filament diameters in the micrometer range and interfilament spacings of a few tenths of a micrometer, exhibit a strong proximity effect. The measured power loss at a constant ac field amplitude and frequency showed an unexpected time dependence on a very long time scale of hours, compared to the ac field cycle time being in the millisecond range. The measured loss vs time curves were found to depend sensitively on amplitude and frequency of the ac field, and in the way the ac field was switched on. The effect can be rather large, changes of losses by up to 60% were found. Losses can increase or decrease with time depending on the structure of the sample. As an independent check losses were also measured by a magnetization method. The results were in very good agreement with the calorimetric measurement. The effect of time dependent losses is qualitatively explained by the slow decay of proximity currents which are induced when the ac field is switched on. They create a time dependent bias magnetization, which influences the ac losses.