You don't differentiate anything for consumer rights.
If you advertise and charge a monthly fee for a service, you don't need to support it forever.
If you advertise and charge a one-time fee for "premium gold star membership" on your site, then you need to support it for the lifetime of your site, not forever.
But if you advertise and charge for a product or content, saying "Buy it now!!! Own this beautiful widget for only $9.99!" then you have the following options:
a) Hand over the product, take the cash and be happy;
b) Instead of handing over the product, promise to show the product on demand, and keep your promise eternally;
c) Sell a promise to show the product on demand, but don't actually do it - that's called fraud and should be prosecuted.
But noone is asking jmanga.com for eternal support - they can quit, but they have to deliver the paid-for goods if they want to stop providing on-demand access.
b) regular open source apps that they don't have a community to continue them after the original coders lose interest, and you don't know enough programming to support them nor have the money to pay someone to work on them?
b) is like saying 'how is this any different from a car if you drive it until it runs out of gas, and then push it into the ocean, and then wait until it rusts from being under the water, and then you forget where it is?'
Yes, of course it is possible to deny yourself the ability to view content, use software, or access goods that you have purchased. That is beside the point, which is that webapps are inherently transient - unless you have access to the ability to configure and run your own server to host the application, the ability to use it can be revoked at any time, either through malice, negligence, or the regular operation of business. There are numerous examples of all three categories. This is, in fact, worse than proprietary software. At least with proprietary software (DRM/authentication notwithstanding), you have an executable, and it works on the machine you have right now. VM software like VMWare allows you to preserve a particular software configuration indefinitely if you wish, and access that software as long as you like.
If I launch a web-app for example I don't necessarily want to have to support it forever.