Earlier quoted context omitted.
A couple of months at least. It could take more than a couple of weeks for many users to realize the service is shutting down (skip past the email in their inbox, etc.) Even if a user receives notification with the full two weeks notice, they could be on vacation and unable to download the files. They could figure "Oh, I'll make a note to download my stuff when I get home from work" then forget all about it.
What if their development team found other jobs, giving the standard 2 weeks notice. Who will maintain the servers and code for those few months? Sure, the code allowing for the export of data might seem trivial but you still need someone to maintain the system. It's almost guaranteed to need some kind of attention over a couple of months in use. Especially if the export feature was written quickly after the announce…
At the very least they could be open and honest about what is going on instead of pulling a "thanks for being part of this incredible journey, we've had our fun so now we will let you stand in the rain".