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Hi, I'm Mike G and I'll be glad to assist you. Your description indicates a bad connection making and breaking due to the heat in a wire with current in it. Check all connections, make sure they are tight. The only other thing would be a thermal protector on the transformer trhat is breaking the circuit due to overheating.
Not necessarley, check the connections first. If you are using a dimmer for the lights, the transformer may not be the type that is listed for dimming. Check the label for that. A non rated transformer will fail on a dimmer due to the low voltage.