Actually, I just figure it out. I hadn't passed it the header info. So I did the
following:

data_hdr = dataset.nifithdr
NiftiImage(orig_s1_map,header=data_hdr).save('searchlight_results.nii.gz')

And it worked beautifully.

I just tried your suggestion, and it (of course :) ) works too. 

Thanks for the quick reply!
Amy