There are many possibilities, however let's consider just two.

One is related to the TCD itself. I once observed a TCD which was not grounded properly, and would display fluctuations in signal as a result. These were not as chaotic as you might imagine, however what you are describing seems a little more systematic in nature, and is probably related to the material.

It is possible that during the synthesis, and subsequent catalyst pretreatment/activation process, residues remained on the material surface. These residues may have blocked some of the surface sites from interacting with and converting the CO2. However, these residues were either consumed by the inlet composition during a chemical reaction or decomposed as a result of the inlet composition/atmosphere, as a result freeing up more surface sites of the catalyst to interact with and convert the CO2, which would explain the increase in conversion of CO2 with the initial time on stream. Afterwards, the material simply could have been losing some of its SSA, microstructure/etc. as a reuslt of performing the reaction or the operating conditions themselves (i.e. temperature/pressure), which would cause a decrease in activity with respect to time on stream.

I will explain what I might do in light of the two possibilities outlined above. You need to first ensure the quality of your instrument/test method. If this is not an issue, next you need to devise some experiments to try and figure out what is going on. A nice start might be TGA to represent the synthesis condition; if an unreasonable amount of mass is lost you may have unreacted precursor. If this is not the case, you can further use TGA and test your material in as similar an atmosphere as possible as your reaction environment, with as similar a contact time used in your reactor as possible, again examining for mass loss initially to explain the concomitant increase in activity. If there are no mass changes after this, it is very likely the microstructure or SSA of your catalyst is degrading which explains the decrease in catalyst activity. If you begin to see a SLIGHT mass increase, then that could mean you are accumulating part of the reactant on the material surface in some way (i.e. iron metal to iron carbide, for example), blocking the active sites from converting additional CO2.