TURNING IT AROUND
Keep your mission statement prominently displayed
I've seen some projects where there's a great mission statement that is developed in order to sell the project, and then it's put in a drawer for no one to see ever again. Ensure that you are re-visiting and re-communicating the mission statement throughout the life of the project to ensure that you're doing the right thing, that everyone understands what the right thing is, and that you're driving toward resolving the problem.
Adjust the mission if the problem changes
Problems aren't immutable; they can change in complexity and importance. If something changes about the problem, make sure that your mission changes accordingly. This could also mean that the importance of your project changes because the problem is either more or less important than it was prior to the change.
Put it on hold
If you can't get support for the project, either put it on hold or recognize that it's not something that sponsors care enough to address at the present time. Better you do this than try to forge ahead with the project without sponsorship. It's likely only a matter of time before the project dies.