What are the specs of the tif? ie: number bands, pixel depth?
How are you doing the export? Are you right clicking the tif and choosing >> Export?
Are you prompted for promoting the pixel depth for adding NoData pixels? If so, choose No (no promote, export).
There is the source of the problem. A jpg file format can not support 32 bit. Can you convert your 32 bit tif to an 8 bit unsigned tif prior to attempting a jpg conversion (do you need 32 bit data type)? Are any other file formats supported by the other software?
for information regarding raster file formats, see: http://resources.arcgis.com/en/help/main/10.2/index.html#//009t0000000q000000