Yes, broken neon signs can be repaired. Neon signs are made up of many sections named as units. Even if one of the units is broken, you can repair that unit or make the unit with new glass. Repairs means a new glass is heated and then melted to original piece of glass. Once this unit is fixed, you can refill it with gas. Some shops do not repair units that have argon-mercury units in them. If Neon sign has many breaks it will not be cost effective to repair it.