Is it possible for a monopolistic firm incur losses in the short-term or longer-term when attempting to maximize profit? Why or why not?

A monopoly could theoretically earn negative profits in the short run, due to shifting demand -- but in the long run, such a firm would shut down, and therefore no monopoly would exist.

A monopoly maximizes profit by choosing the quantity where Marginal Revenue (MR) = Marginal Cost (MC). In the short-run, if this quantity has an Average Total Cost (ATC) greater than the corresponding price on the demand curve, then the firm would earn negative profit ([Price - Average Total Cost] x Quantity).

I am not aware of any practical examples of this type of situation, but it's a great question -- and I would love to see an example, if anyone has one. I think the closest example might be a monopoly that becomes obsolete with the development of a new technology or substitute product. By definition, no substitutes exist for a monopoly, so the monopoly would cease to exist just as it might experience a loss.