Hi carrie -- some of the hardest problems to deal with are morale problems. They tend to be self-feeding and they take the organization down into a hole that's very hard to climb out of.
First, clearly define the problem. Are they overworked, under appreciated, both, something else? Are the expectations of job performance clear and reasonable -- or even achievable?
Second, who are they taking their complaints to? Do they complain to you, each other, upper management? NO ONE SHOULD BE ENCOURAGED TO COMPLAIN TO SOMEONE WHO CANNOT BE PART OF THE SOLUTION!!! Did I say that loudly enough? Low morale usually means folks are complaining. It doesn't mean they don't have valid complaints, it usually means that they don't feel heard. Generally, that's because the ones doing the talking (complaining) tend to complain laterally which is completely ineffective and makes the situation worse by forcing workmates to get involved and take sides.
Third, what is the response of your management to the morale problem? If they are aware of it but unsympathetic or unresponsive then it will continue to fester and people will eventually bail on the organization. If they are aware, sympathetic, but can't offer a solution then keep the fire on them. It's their responsibility to make sure the staff feel like an integral, valuable part of the organization. If they are unaware then there is a gap in the chain-of-command that needs to be filled so that vital information can flow in both directions.
I've long felt that the best work is done by people who feel their efforts are valued and the environment is conducive to a productive goal. An environment of poor morale stems from a poor work culture and is in everyone's best interest to fix.