BPL's going to be fine - especially with the new revenue model.
Consider the situation with membership fees. BPL has relatively fixed costs of creating interesting articles and they need to sell enough memberships to pay for that. If the membership drops too low, it may not possible to pay for articles and the site could fold. With membership fees, it doesn't work to scale the content to match the subscribers (ie. write less articles if less subscribers) because you hit a negative feedback cycle where if you drop the articles then even more people will leave, so you have to drop the articles even more, then everyone stops paying and then you're out of business.
Conversely, the ads monetize a portion of the site that costs relatively little to maintain (or should cost relatively little), thus with Google Ads the forums are almost guaranteed to be profitable, whereas before the forums were unprofitable because no one wants to pay membership fees for a forum. Thus in some form, BPL is almost guaranteed to be around now - even if it is just the forum. Rather than the forums being a drain on BPL, they'll be a profitable part of the site and actually enable BPL to generate more content. And of course with more quality content comes more subscribers, and thus you hit a positive feedback cycle where the site gets way better as they can invest more in content.
Not that anyone asked, but here's what I think BPL should do:
1) Make forum membership free. You'll get more lively forums with free membership and an overall increase in revenue because more ad clicking will go on. I know there was some spam problems with free memberships but those are easily solvable with other techniques (ie. incorporate a question during sign up that requires intelligence so computers can't do it).
2) Optimize ads so they're more profitable and less intrusive. For example, putting an ad at the bottom of the page is more profitable than in the sidebar, because no one looks at the sidebar while they are reading. When people get to the end of a page they're looking for something to click on, so an ad there does very well.
3) Consider making all the articles free. This might sound crazy, but it's how 90% of websites do it. With free articles there would be a huge increase in the number of readers. It would take a little time, but readership would go way up. Another option is a hybrid approach where membership is reduced to say $10 and members can read the articles immediately, while after a month they become open access. In the long run this seems way more profitable, as the vast majority of BPL's excellent catalog of articles is sitting there barely being read because it's closed access and most of the members who are going to read it already have. By opening it up, search engines would direct traffic to these articles for years and they would all chug along generating a few bucks a month each, which collectively can be a lot and thus support new content.
Ultimately, BPL's got an awesome website going. The contributors are awesome and if BPL can monetize it ideally so they're able and excited to generate top notch content then it could become better than ever.