Diabetic neuropathy can't be fully reversed, but peripheral nerves do (slowly) regenerate. How well they regenerate depends on the specific type of damage they take (having a nerve completely severed is worse than slow inflammatory damage), how much damage they take (6 months of uncontrolled diabetes is less bad than 40 years of uncontrolled diabetes), and how old a person is (the older someone is, the less regenerative capacity there is).
There are some type 1 diabetics with neuropathy who get insulin pumps, maintain excellent sugar control for a decade or more, and have a complete remission of symptoms. There's still invisible nerve damage that can be seen on imaging, but the nervous system can sometimes reroute or work around faulty connections - similar principle to a "silent stroke" where you can see an infarcted area in someone's brain on an MRI, but they have no strength deficits, language issues, etc.
As far as chemotherapy-related neuropathy, prognosis depends on how long someone was on a neurotoxic agent, the total dose they got, the specific agent used (the -platins generally have a worse prognosis than some other agents that can cause neuropathy), and if the patient starts experiencing symptoms, whether the symptoms are quickly caught (better if discontinued or stopped immediately once symptoms appear rather than trying to soldier through, unless that is the only agent appropriate for that type of cancer).
