Maybe I'm not understanding the situation, but what Old John described as an "overflow" sounded like a natural spillway. If the spillway is accomodating the rainfall, then what is the problem? If it is not, then yes, a dam problem may be imminent.

By accomodating I mean the spillway carries sufficient excess water to prevent the water level from ever reaching or exceeding the dam height.

Has your water level ever reached or exceeded the dam height?