The best place to fix it is where you bought your hearing aids. They are certainly supposed to give you some support services. It’s usually for free at the beginning, or they might charge you if your warranty expired.
I certainly wouldn't try and fix it by myself. It’s too tiny and delicate, even if it’s just a nylon thread. Exactly for this reason, it shouldn't be too costly to fix it on any fixing lab, either where you bought it or any other place that deals with hearing aids.
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