This is not on-topic for Super User.
This is a question about what you can do to continue receiving historic benefits of a subscription service without a subscription. It is not a question about computer hardware or software.
If you wish to be able to download and permanently keep these files then you should discuss how to go about that with the company itself.
My reasoning for why I do not believe this is a problem with actual software is because your access to the files is predicated on you having a subscription.
It is a question about a web-based subscription service to rent access to magazines. There is no Windows app outside of your web browser, and the browser is simply a viewer. You are not paying to download media such as epub files, or mp3s or movies, you are only paying to view it.
If you had purchased each and every issue at market price then it could be a matter of fair-use and effectively creating a backup, but as it is a monthly service to read as many as you like then I do not believe fair use applies here.
If you had bought specific content and the company gave you the files but kept a key so that they could restrict the number of places you could view that file then it can be argued that should that company go out of business then you should still be able to access that file. In that case you would want to be able to remove protections from that file. That is reasonable and allowed on Super User.
But you are not buying specific content, you are buying nothing more than temporary access to content. Circumventing DRM in this manner is not okay.
This is similar to the fact that subscribing to Spotify for a month does not give you unlimited access to download their entire catalogue for permanent personal consumption.