I'm quite certain your purchase history is stored in Nintendo's servers; there is an off-chance they could connect your ID to a new piece of hardware if you sent it in to them to allow you to re-download. But the point is that you cannot simply log into your Nintendo Network ID on a new/different system on your own. You can only do a System Transfer, and that requires your old hardware to still be functional. My older brother ran into that problem.
Even in a PSN-esque login situation, though, all servers come down eventually. Sony does a good job of keeping their past hardware supported but I am quite certain the day will come that I am no longer able to switch between my US and Japanese PSN accounts on my PSP. When that happens, my US PSP digital games are toast.