Will the monopolist firm continue to produce in the short run if a loss is incurred at the best short run level of output?

A monopolist firm can earn losses in the short run if the price is less than the minimum of AC. But if the price falls below the minimum of AVC, then the monopolist will stop production.

In short run the firm tries to recover at least the minimum of AVC, so the firm will continue to produce when the price is between the minimum of AVC and the minimum of AC.