"Conure Bleeding Syndrome" is suspected to be caused by a lack of vitamin K.
Vitamin K
Function: Vitamin K ensures proper blood clotting through the manufacturer of prothrombin (the factor in blood that causes clotting). Synthesis occurs in the intestines. this is true in both mammals and birds. Vitamin K is vital for the proper liver function. Most diets have adequate vitamin K.
Symptoms of a Deficiency: A deficiency in vitamin K can cause a bird to bleed to death. Anemia, as well as blood and vascular disorders, can occur due to vitamin K deficiency. Deficiencies can also result from prolonged antibiotic use.
Symptoms of Toxicity: Not reported in birds, but in humans can cause brain damage and red blood cell breakdown.
Found: Vitamin K is found predominantly in green vegetables, including broccoli, cabbage, asparagus, peas, green beans, turnip greens, spinach, and cheese. It is also produced by bacteria in the bowels.
pg. 47 of the Healthy Bird Cookbook
I've had no experience with "CBS", let alone heard of it.... But here are some links that mention it...
http://theaviary.com/s1295-09.shtml
http://www.cyberparrots.com/gcconure.html
http://www.californiaavianlaboratory.com/anemia.html
Conure Bleeding Syndrome (CBS) appears in conure species with rapid onset of weakness and somnolence. The patient may be bleeding from the mouth or cloaca. In some cases, the hemogram suggests responsive anemia with no visible bleeding, consistent with internal hemorrhage. Cytologically, CBS appears similar to changes seen with lead toxicosis. This syndrome may be due to a calcium deficiency, which is supported by a finding of hypocalcemia in a historically calcium/Vitamin D3-deficient bird. Clinical response to parenteral calcium strengthens this hypothesis.
http://www.northforkanimalhospital.com/animals/birds/birds_conure.htm
Ihr Internet-Portal
Basically pointing out to the fact that a bad diet can cause this... where-as as long as your conure is eating healthy, you should not have any issues.