You have more template dna and primer in the multiplex compared with the single pcr. It may be that there is a pcr inhibitor in the dna which affects one pcr more than the other. Inhibitors often work by removing Mg from the pcr mix. I would try increasing the Mg concentration to 2mM or even 2.5mM and run dilutions of the mixed templates . 2 or 3 dilutions maybe 1:2, 1:4 and 1:8 of the dna sample. I am assuming that there is not a strong primer dimer band which may be removing one or both primers from the failing pcr set

Run singleplex controls alongside the multiplex reaction to confirm that each primer pair works under the same reaction conditions. Verify that the primers for each virus are specific and do not have significant cross-reactivity or form primer-dimers. Start with equal primer concentrations and adjust based on the initial results. Decrease the concentration of the primer that is amplifying more efficiently. Start with equal concentrations of primers (e.g., 0.2 µM each). If one target amplifies better than the other, adjust the primer concentrations (e.g., increase the concentration of the weaker primer pair)