There are at least a couple different designs of oven control systems for gas RV ovens. Most or all new ones work with a fairly typical pilot light setup similar to most other gas appliances with pilot lights, i.e. the pilot heats a thermocouple which controls the gas flow to it and, along with a thermostat, to the main burner. On these, you do have to hold in the control for several seconds to light the pilot, until the thermocouple gets warm enough to allow things to stay lit on its own. I don't think this is the system your oven has, though.
The other system I'm aware of uses two valves, a themostatic valve and a safety valve. On this, the pilot light when no heat is required is a tiny little flame, not much larger than a pin head, and the amount of gas needed for it to burn flows whenever the pilot is on (with no thermocouple to shut it off). When heat is required, the thermostatic valve does two things: it increases the gas flow to the pilot, making the flame grow, and allows gas to flow to the safety valve. The safety valve has a sensor bulb near the pilot flame, and the larger pilot flame warms this sensor bulb up and causes the safety valve to open and let the gas flow to the main burner. When the correct temperature has been reached, the thermostatic valve closes the gas flow to the safety valve (and burner) and shuts the pilot back to its small flame size, and soon thereafter the safety valve closes as its sensing bulb cools down.
It sounds as though your thermostatic valve is working properly, but the safety valve is not opening, either because it's defective, because the sensing bulb for it is not positioned properly, or because you aren't waiting long enough (it shouldn't take too long to open, though--no more than perhaps 30 seconds I'd guess, and probably less). If it's a defective safety valve, you may well find that replacements are not available new any longer as it may use a mercury bulb for its sensing element, in which case your best bet may be to find a used one...or replace the whole range with a new range.