It may well be a problem with Biturn. The basic problem is probably that your surface normals are wrong - and that is something Biturn does occasionally have a problem with. Frankly you may just be out of luck (I have a few models I've never been able to convert successfully

) - but here are some suggestions.
1. Double check the imported object to make sure everything has "is showing" true and does have a texture. Simple - but errors happen here sometimes.
2. Check to see that the object does preview in Biturn correctly and that the conversion doesn't give any errors.
3. Another free (but no longer supported) program that outputs .ase is 4DBlue (
http://www.4dblue.com/). You might try that.
4. Wings 3D (
http://www.wings3d.com/) has one of the more reliable exporters. You could see if that works.
5. Finally - as a last resort - if you
really 
want the object. An .obj file is just a text file and the format is described on several web sites. You could try checking and correcting the surface normals manually. I've done this successfully for very simple models just as a test - but personally would just give up before this point.