This "mystery illness" isn't such a mystery.

From India:
Acute flaccid paralysis (AFP) is a condition in which a patient suffers from paralysis that results in floppy limbs due to reduced muscle tone.

[link to www.livemint.com]

Could it be this is what's happening in California?

"Symptoms include loss of the ability to move limbs, which leads to atrophy and causes muscles to shrivel. "They just dangle, like empty balloons" Van Haren said."

[link to news.yahoo.com]

So what causes it?

"Two doctors from Delhi’s St Stephens Hospital, Neetu Vashisht and Jacob Puliyel, who compiled data from the national polio surveillance project, found a link between the increase in dosage of polio vaccination and the increasing cases of NPAFP".