Is it really possible to repair bad sectors?

what do you value most 50-100EUR/USD or your data?

backup often. and for primary storage anyway use something you have a little bit of trust. disk get broken - it's a question of when, not if. bad sectors are indication that end of life is soon.

I have used Spinrite to save drives others have thrown out due to "bad sectors", they are still running today. Thanks for all the free drives guys.

I guess it comes down to the definition of "bad sector"

A sector can get marked as bad when it just cannot be read reliably anymore, spinrite fixes these issues, and they are far more common than actual bad sectors (as in damaged).

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It basically depends how bad is it. A single bad sector (confirmed by software like MHDD) is a warning, if it is reallocated after a write, the drive could work for many months. On the other hand if it has few bad sectors, the drive is shot, buy a new one.

You should monitor SMART data and run smart test at least weekly on any drive that has data you care about.