In looking into that rabies post from earlier today, I came across a table a table of rabies cases in the US. This part of the table stuck out to me, so I looked into it further:

May 3, 2004 AR Bite (organ donor) Bat, Tb
June 7, 2004 OK Liver transplant recipient Bat, Tb
June 9, 2004 TX Kidney transplant recipient Bat, Tb
June 10, 2004 TX Arterial transplant recipient Bat, Tb
June 21, 2004 TX Kidney transplant recipient Bat, Tb

In 2004, an organ donor donated organs that led to the deaths of 4 recipients. The doctors didn't know the donor had rabies, and didn't test because his symptoms corresponded with the drugs they found in his system. They assumed he died of a drug overdose.

[The surgeons] thought he had suffered a fatal crack-cocaine overdose, which can produce symptoms similar to those of rabies. "We had an explanation for his condition," says Dr. Goran Klintmalm, a surgeon who oversees transplantation at Baylor University Medical Center, where the transplants occurred. "He'd recently smoked crack cocaine. He'd hemorrhaged around the brain. He'd died. That was all we needed to know."

(Emphasis mine)

That's not the only time it's happened, either.

In February 2005, three German patients in Mainz and Heidelberg were diagnosed with rabies after receiving various organs and cornea transplants from a female donor. Two of the infected people died. Three other patients who received organs from the woman have not yet shown rabies symptoms. The 26 year old donor had died of heart failure in December 2004 after consuming cocaine and ecstasy. In October 2004, she had visited India, one of the countries worst affected by rabies worldwide.

Organ donors aren't often tested for rabies because there's only a short window of time between when the donor dies and when the transplants must begin.