If you can export as one file format but not another, you probably have some type of geometry that's either too complex, or corrupt.
Importing curves directly from Illustrator can sometimes lead to messy geometry that may look visually correct, but might actually have some areas where the curves double back on themselves, criss-cross, etc.
If you were building something like this my recommendation would be to double check all of your curves in the sketch and make sure they are cleanly laid out. Also, if your computer doesn't have enough RAM and it's a very complex piece of geometry, the large file size of the export could crash the program.
Without seeing your actual geometry those are only guesses.