Hi Tangofan
This is likely due to geometry that is too complex to be described well in STEP / IGES definitions.
Check your illustrator file if there are curves with tight bends, a lot of vertex points or overlaps.
Use a remove duplicates script and use simplify path on complex paths.
In Solidworks, always make sure that surfaces are offset a bit from surfaces on the target.
Also small radii and complex fills often cause errors in exporting. I hope that helps.
If all else fails install an evaluation version of Rhinoceros, those exporters work better.