Hello,
Thanks for reaching out and it's great to see you've been with us since QuickBooks Pro 2015. I know sticking with the product you have is always nice, but upgrading to the newest version, QuickBooks Desktop 2019, will give you access to features that your business may benefit from greatly. I'm also happy to clarify our supported products.
The agent was correct about Intuit only supporting and having downloads to the most recent three years of the product. This is done because over each edition, new features are added and improvements are made to the software. Our goal is to ensure that our users have a product that works correctly as we know how vital QuickBooks Desktop can be to running a business.
Since the download link you have isn't working, another thing I recommend looking for is the install file on your computer. If you still have access to that somewhere, you should be able to reinstall the program. Otherwise, upgrading to the newest version, Pro 2019, is the way to go. If the agent didn't go over the new features with you, take a look at the What's new in QuickBooks Desktop for Windows 2019 article to learn more.
I hope that helps. Let me know if you have more questions!