We study the mobility of objects embedded in an immersed granular packing and subjected to cyclic loadings. In this aim, we conducted experiments using glass beads immersed in water and a horizontal plate subjected to a cyclic uplift force. Tests performed at different cyclic force frequencies and amplitudes evidence the development of three mobility regimes whereby the plate stays virtually immobile, moves up steadily or slowly creeps upwards. Results show that steady plate uplift can occur at lower force magnitudes when the frequency is increased. We propose an interpretation of this frequency-weakening behaviour based on force relaxation experiments and on the analysis of the mobility response of theoretical visco-elasto-plastic mechanical analogue. These results and analysis point out inherent differences in mobility response between steady and cyclic loadings in immersed granular materials.