Anytime I have ever seen a repair on the dam for water pouring out it always has come down to a backhoe to dig out the area and find both the incoming and outgoing water spot(s).
Once you have it opened up, pack it back with clay, top with topsoil and plant some new grass seed.
Water is a wicked thing when it comes to erosion. If it twer me...I'd be getting on that leaky spot on the double as it will only get worse with the water pouring out of it.
GL on the repair.
