You are looking at two states:
You note that in every other example, the second state dominated the first.
But there are actually three states:
- Healthy, never-infected.
- Healthy, cured.
In every other example, an infected shifter infected a healthy, never-infected shifter. I.e. the second state still dominates the first in this list. But Odo is in the third state. He was previously infected and is only healthy because he was cured. Apparently the cure persists after the disease is eliminated.
This behavior is consistent with how real diseases work. When a healthy person encounters someone with (for example) chicken pox, the healthy person can catch chicken pox. Once the sick person recovers, that person can neither transmit nor catch the disease again.
It is unsurprising then that Odo doesn't become sick again. He's still cured. It's also unsurprising that he can transmit the cure. Left indeterminate is what happens if a healthy shifter were to link with Odo. Would that shifter change from the first state to the third? Or stay in the first state? Either seems possible.
As you note, we are never told that the disease and cure work this way. But it is a reasonable way for it to work and is not contradicted by what we are told. Prior to the final episode, they could have had it work the other way. We only learn that it works this way from observation.