It's not a strong shekel, but a weak (and dying) dollar. There are rumors that US banks are already limiting the daily withdrawal amounts.
Shekel Strengthens Despite Interest Rate Cut
(IsraelNN.com) The shekel has strengthened against the dollar despite Monday night's surprise half a percent drop in the Bank of Israel interest rate. Bank Governor Prof. Stanley Fischer previously warned that reducing the rate will not necessarily satisfy exporters, who have said their profits are falling because of a strong shekel.
Following the interest rate reduction, the shekel-dollar rate jumped to 3.64, but the sagging American dollar sank again on world markets Wednesday, setting the shekel rate back to below 3.61.