I am so sorry that your father's cancer has turned so aggressive. He is fortunate that you are looking out for him.
You asked if that kind of increase had been seen before. The fastest PSA doubling I have learned about from a reliable source is every two weeks, which, depending on the exact dates, is roughly what your dad is experiencing: 104 to 208 in 2 weeks; 208 to 416 in 4 weeks; 416 to 832 in 6 weeks; 832 to 1664 in 8 weeks. The expert discussing this was talking about more than just one patient; he was describing the end of the range from slow to fast of PSA increases that can occur.
I'm surprised at the doctors' surprise that such an increase would occur despite steroids; I just haven't heard much about steroids as a primary medication to hold back aggressive prostate cancer, but possibly another Board participant knows more about such use. Usually we hear of a steroid being used with chemo.
I can give you some general thoughts without further information, but it would help to know key facts about your dad's case. Because he has been on steroids, I'm guessing that he has had chemotherapy for prostate cancer. Is that so? Has he been scanned for bone and soft tissue metastases (such as in the lymph nodes)?
Has he had hormonal therapy ("androgen deprivation therapy")? I'm guessing that he has and that at some point such hormonal therapy failed to control the cancer. If he has not had hormonal therapy, that would be the logical first step to me, as a layman. Even if he has had hormonal therapy in the past, it might be worth trying it again, especially as there is at least one impressive new drug that could be tried. Your dad may well qualify for the new hormonal medication known as Abiraterone (Zytega), which acts very quickly and effectively. Do you know if his doctor considered this? Do you know what kind of doctor he is seeing? I'm thinking a "medical oncologist" would likely be a much better choice than a urologist, for instance, at this point.
Hormonal therapy often reverses and eliminates some pain rapidly, sometimes within hours. Sometimes this is done with surgery (orchiectomy).
It's hard to think about the prognosis without knowing more about his case. (By the way, I was diagnosed with prostate cancer in December and given five years to live; but that was back in 1999, so when I hear a prognosis for a prostate cancer patient, I take it with a huge grain of salt.) I suspect that your dad has at least some chance to beat this latest challenge and to go on enjoying life.
Also, there are a few expert doctors using advanced techniques that sometimes work spectacularly well at pushing aggressive cancers way back. However, it's sometimes difficult to get expert medical advice plus insurance to cover these treatment (for example, Leukine, Provenge). One outstanding book that can help orient you and your dad is "Beating Prostate Cancer: Hormonal Therapy & Diet," by Dr. Charles "Snuffy" Myers, MD. He gives several case history examples that involve PSAs in the thousands with good outcomes.