Yes, SSHL can be cured. In my observation, homeopathic treatment has been successful in the majority of cases. Unfortunately, I am not aware of any formal scientific studies to corroborate this.
Khalilzadeh S, Vaghasloo MA. Relapsing Sudden Hearing Loss Treated and Prevented with Principles of Persian Medicine: A Case Report. Traditional and Integrative Medicine. 2019 Sep 24:117-22.