I think this is also an issue with other magazines from other companies. I have a digital subscription to another magazine and find the digital copy not half as handy as the paper copy, while the paper copy would come via surface mail from far away and be much more expensive. I will not renew that digital subscription, but, as you found, I think I will lose the ability to access the digital copies.
So it seems as though we buy access only and not actually a copy of the magazine.
For the magazine to which I subscribed, I have already decided that the content is not worth the continued subscription, so that solves the problem.
This, of course, is the software subscription problem, where software companies are moving rapidly to a subscription basis where you get to use the software, but only as long as you pay the monthly subscription. The accumulated cost is very high indeed, but you are effectively paying a ransom to be able to continue to access the files you create using the software. Local copies of files are fine, but if you can't access the software to open the files, you will be stuck.
Can you download the issues as PDF files?
Is there a Kindle version available, because there is no annual subscription for the device, and the files are added to your perpetual "cloud" storage area?
Marcus