Contibutions that exceed budget

Members on occasion designate a portion of their offering for a supported ministry that exceeds the budget. What should happen with the excess? Seems to me that the church has an obligation to use the funds for the ministry and not allocate the excess to the general fund. Also, if a donor knows that the excess is being allocated to the general fund and not used for the designated purpose, there is a possibility the donor will not give except to general fund. Comments please.