What kind of HW Heater is it? I have an Atwood, 10 gallon, with a mixer on the outlet side. The HW heater is designed to heat the water far above safe temperatures (180 degrees, I believe), and cold water is mixed in at the back of the heater to bring it down to around 120 degrees delivered to the faucets. Net result is the equivalent of a 16 gallon tank. Works great, unless the mixer gets plugged which is what happened with us. In that situation, the symptoms are exactly what you describe as your problem. Water starts out hot, but cools quickly. If you don't have that type of HW heater, I agree with the others that your most likely problem is an open faucet somewhere... most commonly the inside or outside shower. Good luck.
2008 Jayco Designer 35RLSA pulled by a 2007 Chevy 3500 D/A SRW