You may be thinking to yourself, "that's not me!" or "I've never heard anyone say that!" And maybe that's true.
But consider this: if people experience you as unapproachable, how likely is it that they feel comfortable giving you honest and open feedback?
So, let's assume it's possible that some people find you somewhat unapproachable some of the time. Let's also assume that, if you're being unapproachable, perhaps it's for good reason! Maybe you need a little uninterrupted time to get a pressing project finished or you need some head space to deal with a personal issue -- and you need people to leave you alone. If that's the case, but you haven't figured out how to advocate for your needs, you're likely to push people away permanently. You might get the space you need right now, but it will come at the cost of your relationships, credibility, influence and impact.
So what can you do instead?
1. Get feedback on your unintended impact you have on others.
There is often a gap between your intention (what you're trying to say or achieve) and the impact it has on others (how they experience what you're saying or doing). Ask a few people whom you trust to give you honest feedback to share how they experience you -- especially under stress.
You might say, "I understand that some people experience me as hard to approach, especially when I'm under stress. I believe that's true, and I want to change it. Can you share with me what you've noticed that I might not be aware of? It would help me become a better manager and colleague." And then, when they do give you feedback, thank them!
2. Ask for what you need rather than acting out.
Try saying, "I need a few uninterrupted hours to wrap this project up. I am going to close my door until 3 pm so that I can focus, and then I'll be available." This way, you'll be viewed as assertive and considerate, rather than unapproachable.
3. Address unapproachable behaviors in others -- across the board.
You may be likely to ignore a high performer who makes himself difficult to approach because you value the quality of his work. People notice that. It's not enough to work on your own approachability; you need to make sure that your entire team is seen as easy to do business with.
You don't need to make yourself available to everyone every minute of the workday. But you do need to make yourself the kind of professional who is seen as inviting and inclusive of other people and their ideas.