Sorry, I can’t replicate the problem. I’ll assume you’re setting the export to EPUB 3.01 (not EPUB 2).
Corner effects on image frames are maintained by default. If that’s not true for you, please let us know which version of ID you’re using, and maybe link to a couple screen shots, one of the image in ID and one of the resulting page in the epub. Be sure that in the EPUB Export Options dialog box you’ve selected Preserve Appearance from Layout, which is turned on by default.
If you’re talking about a stand-alone text frame, rounded corners are supported automatically, which is pretty cool. For other corner effects, you’ll have to rasterize it (convert it to a graphic) to maintain the effect. In recent versions of ID (I think CS6 and later) you can select the frame that has the corner effects and choose Object > Object Export Options and set it to rasterize container on export.
hope this helps!
AM