The answer is rarely "not possible" but rather "not possible without custom code that is probably not worth the effort of developing". Either is a valid answer if it is true, and that can help people who have the same problem. So if it turns out to be impossible by all means say so as an answer. I don't see any problem in leaving questions "hanging around" if they have useful information.
If it turns out that there is some peculiarity or something specific to your environment that is unlikely to occur generally then I would say close it or delete it. For example you have a question "why can't I navigate to my team site" and it turns out the network cable was unplugged by the cleaner - that should be closed because it wouldn't really help anybody else (unless they had a clumsy cleaner).
Remember to up-vote answers if they are helpful - they don't have to be perfect. It encourages people to post valid answers, and if we all do that we increase the chance of getting some answers to these questions.