I've had this problem for years, and I have a support request in. The only work around that I actually tried and got to work today, was to install Illustrator CS3 (beside my up-to-date CC). When I opened the AI file in Solidworks, it started CS3, and finally imported the profile I had. The downside to this is that the CS3 needs to be the default Illustrator version. If you change the default program to open AI files back to the new version, I get the error message again.
The other option that I've been doing is to export the profile from Illustrator as a DWG, and opening that in SolidWorks. It seems to work okay.