use save to devices, the image must be hanging off the art board. when you export it crops.
I tried that, but it didn't work... the strange thing is... it really isn't hanging off the artboard, there's plenty of room! The background is transparant.
I'll attach the image.
Con Brio ster (35x35).ai 1.0 MB
What cs are you using? I attached your art back to you. You can click off the transparency in save to web.
You will have a solid background. But the art you sent covers the whole art board. So that should not be an issue.
You may want to hard restart your illustrator or delete the preference to get back to default preferences.
Then retry to export to png or save to web and devices compression to png.
Look under your illustrator help menu.