The practical application of formic acid production through the hydrogenation of CO2 has garnered significant attention in efforts to tackle the challenges associated with (1) achieving net-zero production of formic acid as a chemical feedstock and (2) improving hydrogen storage and transport. This study focuses on demonstrating the continuous operation of a trickle bed reactor for converting CO2 into formate using palladium on activated carbon (Pd/AC). Optimal temperature conditions were investigated through a dynamic operation for 24 h, achieving the maximum productivity of 2140 mmolFA·gPdsurf.−1·h−1 at 150 °C and 8 MPa, with an H2/CO2 ratio of 1:1; however, catalyst deactivation was observed in the process. Stability tests performed under continuous operation at 120 °C and 8 MPa with an H2/CO2 ratio of 1:1 indicated a gradual decline in productivity, culminating in a 20% reduction after 20 h. A comprehensive analysis comparing fresh and spent catalysts revealed that the diminished catalytic activity at elevated temperatures was attributed to the partial sintering and leaching of Pd nanoparticles during the hydrogenation process. These findings offer insights for the future development of novel Pd-based catalyst systems suitable for continuous hydrogenation processes.