Google Reader was a product that was crazy cheap to maintain (no way it had more than a dozen engineers working on it), and it was used primarily by the extremely online, especially journalists, bloggers, and other sorts of influencers. If they had viewed Reader as a marketing expense, keeping it online would've been a no-brainer.
But instead, they instead viewed it as a consumer tool that didn't have a path to profitability, and they were 100% right, but then over the next few years, it became clear how many later Google efforts would've benefited from Reader existing. Google+ would've meshed well with it. That little Google "stuff you maybe want to see" panel on Android phones that would frequently make little notices like "hey, we think you like this site, there's a new article," and that was probably really involved to build, and also it absolutely sucked compared to just having Reader.
Ultimately I have to assume that it's a business org problem. No engineer was going to get a promotion keeping Reader alive. No manager was going to be able to grow Reader's audience 10x. No director would want to give up a half dozen of their engineers to keep Reader running just because it would significantly hurt Google to turn it off. And no executive cared about a product that small. The org structure didn't lead to someone incentivized to want to keep Reader going, despite its popularity inside and outside the company.