When the Board was named, life was simpler. If you look at the early questions in the archives, it makes sense that things could be answered within 100 hours. But we can't change the name now... it's part of the tradition.
As the Internet took over the world, people became experts at finding answers to their own questions by looking them up (what a novel idea!) Gradually, the questions that people asked the Board got more and more complicated. They required more depth and more time to find answers to. I have 3 questions that I'm working on right now that are overdue by at least 100 hours. But all three of those questions would be virtually impossible for me to answer within 100 hours.
So no, we don't have a limit to how long questions stay in the inbox. Most of us really do try to get things done in a timely manner. Sometimes, questions don't get satisfactory answers unless we take the time to read them thoroughly, think deeply about our answers, and write and proof and edit our answers. And really, it's in your best interest. We totally get that sometimes that means the answer no longer matters, but it may matter to other people too.
For example, you may think that simple 'what's your opinion on ____?' questions wouldn't take very long to answer. Au contraire, mon ami! We care about making sure our answers to opinion questions are nuanced! More than once, I've thrown up my immediate reaction to questions like this and been lovingly rebuked by some of the other writers, mentioning that perhaps I was too harsh, or needed to think about something a little more. Writing a good opinion takes a while.
Also, there is etiquette to the Board. If someone starts an answer to a deep research question, it's kind of rude to take over for them... so even though you notice that something is way overdue, you don't want to step on the other writer's toes if they started an answer.
NOW, that isn't to say that there aren't some questions that are in our inbox that have definitely been in there for way too long. None of us can disagree with that. Sometimes, we hold things over for a ridiculously long time... and we are sorry. Sometimes, we start something, but as we realize how time-consuming it is, we begin to push it to the bottom of our priority lists. We prefer not to think about those questions, so they stay in our box for inexcusable amounts of time.
Some of us are grad students, others are parents, others have full-time jobs. Some of us rely on scholarships to pay for our undergrad degrees so we have to get A's and that takes a lot of work. We promise we're trying, and we don't take forever because we want to. It's just reality. Don't forget, we don't get paid to do research for you guys.
Sometimes, a weeks-old question will get pushed out when we give it a less-decent answer and hope that maybe someone has a correction to add. But we don't like to do that. We prefer to give good answers, so we let things go over hours (probably too often... admittedly.)
I'm also kind of lazy sometimes. When I notice that I get like 10 upvotes tops on a good answer, it's hard to motivate myself to work on something I feel like nobody really cares about. The Board is one of the most rewarding and enjoyable things I do, but also is one of the most severely underappreciated. I get lazy because there isn't really a reward for my work in the end. People sometimes mention how much they like our answers, but lots of the time we get people who criticize us for various things... and that's kind of hard to deal with (for me anyway.)
Anyway, this was all a long-winded way of answering your question. Basically, things are a little bit different and more complicated now than they were when the 100 Hour Board was first conceived. And we apologize for that. We know there are things we could do better... but we also do try hard to give you good answers to your questions. Because we care about you! So thanks for stickin' around and being patient, even though sometimes it's boring and/or hard. Thanks for remembering that we're human too.