If you're sick, there are three outcomes. You can get better; you can die; or you can linger for a long time and then either die or recover. On the way to these outcomes, however, there are usually lots of ups and downs. You can rally, go into decline, recover, and then have a relapse. Some days you feel better, some days you feel worse. That's the natural course for most illnesses, especially if you're under the care of a physician.
All the faith healer needs to do is to have a few canned answers prepared, as follows:
:: If you recover, or start to feel better, the faith healer takes credit.
:: If you rally, but then decline, the faith healer says, "We almost had it! More money, or prayers, please!"
:: If you decline and die the faith healer says, "You came to me too late!" or "You didn't pray or pay enough."
All the faith healer needs to do is take credit for the small successes that occur over the long course of any illness, and blame the sick person for any setbacks.
Now, let me be clear. With the exception of some charlatans I don't think the Jewish faith healers realize they are practicing a deception. For the most part, I think the Hasidic Rebbes and Roshei Yeshova believe in their own powers, and do not intend to deceive. I also think Pat Robertson, the faith healer who tried to run for president as a Republican, fully believed in Jesus's power, and in his own power to invoke it. However, there are Jewish and Christian charlatans (among which I count one particular hasidic Rebbe based on first hand testimony I've been forbidden to share) and they are liars, cheaters, and fraudsters --and they know it.
Search for more information about faith healing at 4torah.com.