Wasn't the virus linked to how often they changed shape, something about morphogenic matrices and whatnot? Odo didn't really do it too often, relative to the other Changelings; I'm assuming here that being in the liquid form counts as constantly "shapeshifting." It was only when he started shapeshifting like crazy when he was working with the Cardassian resistance that he got sick (and he deteriorated much more rapidly than the female changeling, who did the bare minimum of shapeshifting).
Also, and probably more importantly, Odo was a solid for a time after his infection. He didn't seem to get sick that much later than the rest of the link; I figure either the time he was a solid reset the clock for him, so to speak, or it just wasn't counting while he was a solid (doesn't seem to matter that much).