Interesting problem. My fridge is working fine on mains and 12v but not cooling down on gas. The fridge ignites and there is a steady blue flame, but no cooling! Anybody have a clue as to the problem?
How long are you waiting it will take several hours. I did have a neighbour have this problem about 10 to 12 years ago and I took his fridge out. Found the problem to be burner and flue full of cobwebs. Cleared all out and then worked fine.
Make sure that the caravan is level both ways which is somewhat critical with a 3 way fridge being operated by gas. However, some 3 way fridges can be a bit more temperamental than others when it comes to being level so check the level first with a spirit level on a fixed surface (not an item with hinges such as the kitchen drainer glass or worktop that lifts up and down for example).
As you have a steady blue flame it sounds nothing more than a minor problem but if the levelling up doesn't solve the problem then I suggest you follow the advice from birdman101 (above post). However, it does take a few hours for the fridge to get cold but the first place to check is to put your hand in the freezer box which is a good indication if it's getting cold or not.
As the cooling system is common to all three power types, you should be able to ignore that as a potential problem if working OK on electric power.
Gas is often the highest power rated means of operating fridge, so whilst 3 way fridges are notoriously slow to chill down (8 hours plus to operating temps!), operating on gas should be at least as rapid cooling as other power sources.
The burner/flue do have a tendency to soot up/get blocked by spiders webs and bugs, so possible that whilst the flame is apparently burning OK, the heat can't get up the flue to do it's job!
Cleaning the burner/flue is a recommended regular maintenance task (several times a year if normally run on gas), and I guess if you don't regularly run on gas then real chance the flue has become a bug hotel anyway and got blocked!
Often possible to gain sufficient access to burner/flue by removing the external ventilation grills. Quite how they are fitted varies depending on how old and brand.
If you can DIY, cleaning the flue is cost free (so long as you don't break anything! - old burners tend to rust and get fragile! - treat carefully.), so a good starting point with high probability of success.
Think long bottle brushes are one of the favoured ways of cleaning flue.
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