Would replace the power supply, Could be that, If the camera is connected to a PDU could be an issue with the Power connecter not being connected enough... Could be an issue with the camera it self. When the camera comes on it heats up and the protection kicks in to save the camera form deeper damage?
How is the camera connected? RG59? cat 5e and baluns?
Things to check, Connectors, Power Supply if wall wort just replace it with a new one or at least test with a different one if that cures the issue replace bad one.. Could also be an issue with DVR. Try to connect camera to different port if you have other. Even move to different one for testing that is normally being used with different camera right now. What you are doing is double checking that it isn't DVRs input as the cause. If you connect to another port and it works and you connect the other camera to the one not working now and it works. Could be a Configuration issue. At times might want to Reset DVR back to factory and setup again when things don't work. This normally is after you tried all other things first.. I have to do this on my machines every not and again. Some I have in remote locations that have been there for years still working without issue. Hard to point to 1 thing..