A team of researchers including a University of Maryland entomologist has successfully turned the pesky mosquito's sex life into its downfall. By creating what amounts to a sexually transmitted disease specifically for mosquitoes, the scientists unveiled a potentially powerful new weapon in the global fight against malaria.
From the article, it seems like they spray spores onto the male mosquitoes and then they go and spread it to the females they mate with. Furthermore, they suggest that it’s within a 24 hour timeframe.
These things, to me, point to this being less an STD and more a fungal infection that’s spread through close proximity to spores (the kind of proximity you’d get through mating).
It could very well be that by the time the mosquito has mated several times there simply aren’t enough spores to infect the females they mate with, as whatever spores are on the surface have either been sloughed off or have started to work their way inwards.
Ultimately I don’t know if there’s enough information to give you an assertive answer either way, but this combined with the other techniques for mosquito eradication (like sterile males) could be used as a wombo combo to fully eradicate mosquito populations.