Is there a way to solve this?
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Your balance does not only rely on your inner ear, but also on your eyes making out a fix point - preferably not too close, and stable - not the other person also struggling with the pose. You can easily test this with far easier poses, like standing on one leg, with eyes open or closed. So that the pose is hard to do with eyes closed is expected.
Depending on your reasons for wanting to do the pose with eyes closed, you can do the following:
If you find it distracting to have the eyes open, maybe you can change your surrounding so that there are not many distractors in your field of vision.
If you need to do the pose with eyes closed (for whatever reason), you can try training your balance in simpler poses with eyers closed.
Disclaimer: I'm not a yogi, I don't think I could hold any one legged pose with my eyes closed, and all this is just common sense and knowledge aquired here and there.