LP only tank? You say it runs for a while - the pilot or the heat flame? If the heat flame is staying on to heat the water then it may be a valve issue. Check the manual (both coach and water heater) for proper valve setting for normal operation. Depending on brand, cold water usually enters from the bottom (open cold water valve) and exits from top of the water heater (open hot water valve). Close any by-pass valves between these two. If the by-pass is closed, open and close it again, check/feel for proper operation; it may need replaced (happened to me). Also check to see if you have any shower heads, inside and outside, that may have the water valves open and the button on the shower head closed. If you have luke warm water for a short period then it goes cold, this may be the problem. Good Luck.
NRVIA Certified RV Inspector #523
2003 Monaco LaPalma 36DBD - 2013 Honda Fit