What would you say is an appropriate amount of time?
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.
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 announcement was made.
Now, we've decided to maintain a couple of employees for 2 months to support user exports, where will those 2 people work? Will they work from home? Do you have infrastructure in place to allow them full access from home? No? That means they'll need to come into the office. Will it just be the two of them in the office all day on their own? Do they need some kind of HR? What if they find other jobs during this 2 month export process?
What about customer service? People will have questions about how to export the data or what to do with it. Does anyone answer those questions over the next few months? What if those people found other jobs. Do you hire and train someone new just for those 2 months?
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".
There's nothing fun about shutting down a company and putting people out of work. Also, standing in the rain is being dramatic.
Yes, it's expected that a service provide you wait an export feature when they shut down but you also need to consider the ramifications of a company shutting down: people jump ship. And rightfully so. They have families that they need to take care of and looking for another job is #1.
If you're this concerned about being able to export your data, don't start using a company unless they already have data export feature available and publish a detailed user-friendly exit plan in advance.
Presumably, this company sent out emails to everyone notifying them of the closure and export feature. Yes, 2 weeks is a little short but I understand the complicated logistics of extending the export timeline.
Where there's a will, there's a way.
(Though it shouldn't be a problem for those who have it in their sent boxes, but some even wrote on the website sometimes like I did).
Don't the Internet Archive keep some private collections?