As of version 11.0.0 (August 2016) FITS files with a data field in a bit-array format are not being supported in Mathematica. This remains quite unfortunate.
The data types of a FITS file are sometimes described in the header unit. Try using Import["fileName.fits", "Metadata"] to explore your file if Import["fileName.fits", "RawData"] fails.
Attached are two FITS files from the Fermi LAT Gamma Ray space telescope. The data tables in the first (Pass7) file loads while one of the data tables in the second (Pass8) file fails because it contains two columns of data in a 32x bit field format.