Ok.... I've taken a deeper look into this today. I'll be making some adjustments to sickness mechanics in the next patch.
First of all. I don't believe any of you can get your animals to get sick more than once every 5 hours or so on average. I sure it is possible that if you let your animal stay sick for 3-5 hours, you could then cure him before his next 'check' and he could rapidly become sick a 2nd time. The worst of all animals on vulnerability were suffering from a 50% chance to get sick outside of barns every 5-6 hours. The best 'store bought' animals were getting sick with about a 25% chance outside of a barn every 18 hours or so. This was probably a bit too aggressive for those who didn't have a barn, however, once you breed the animals vulnerability down low enough it is entirely possible to have a lineage of animals that has less than a 1% chance to get sick, even outside of barns so this problem was very capable of being mitigated.
I think the largest issue I identified is the 'check' when the animal was out of food. A hungry animal was 700% more likely to get sick than an animal who had recently eaten. What I imagine was happening here is animals were wandering out of trough range, then missing a single feeding, thus giving them the immunity loss and thus causing them to get sick far too frequently. I will go ahead and remove this mechanic for the time being after the next restart as I'm not entirely sure that part was necessary.