Well, hm. The "condition" they have... they die of old age, like every fucking living thing in the entire universe.
Correct me if I'm wrong, but I don't recall green pus like toxins being the result of old age.
That was the result of them obsessively trying to extend their lifespan. Plastic surgery, medication, genetic manipulation, they tried everything. Their bodies were producing toxins because they were living rotting corpses. They also made themselves infertile during the process, which was the irony. Instead of fighting the fact that they would die some day like everyone else, they should have gotten themselves a few kids. But they were jealous and tried to be just like their parents, and almost destroyed themselves with that.
I also think the Ba'ku got older and would eventually die some day, because there was
a certain visible age range/diversity amongst the adults as well. All they had was more time, but they weren't actually immortal.