The tamagotchi saves after every important event,and dieing is one of them,so their is no way that you can get your tama back,you will have to restart it,the download button only works when the batterys run out.
Well you're supposed to press the reset button and press 'DOWNLOAD' WHEN your tama is dying, not when it's already dead! Trust me it's true. I've tried it hundreds of times and it's always worked.