My camper fridge , Engel SRBT-565D Does not run on 12V ?

You are lucky it lasted this long. Replace it. Parts are not available, and if they were, the cost to repair the unit is far more than a new Fridge.

Depends on how often and long the unit is left open, rule of thumb, fridge 4 deg C, freezer - 18 deg C.

Contact Engel - Engel Website

Hi Joanne
Wow, Is that an open question.....
How long is a piece of string...
I get what you mean though...
Only your Engel Service Dept knows for sure.
They see the returns.
Does it have a compressor or is it based on Heating Elements like an RV Fridge.
If you can hear the compressor running inside, you will know. Compressors don't like being tipped on their side.
I have 1 fridge & 1 Freezer in the back storage room that have been running for thirty years. But I don't think they make em like that any more.
Look after it. Keep the vents clear & hope for the best.
Cheers

Does it ever actually reach the temp set? It may just need cleaning and a service so it cuts out at the right temp.

the owners manual will tell you but yes most do

AUTOMATIC AC/DC CHANGEOVER: All Engel Fridge Freezers can be plugged into both AC and DC at the same time. The Engel is smart enough to use the AC while available and then automatically switch to DC when the AC is no longer working. It will also sense the resumption of AC power and automatically switch back to AC making it ideal for high hurricane areas and places where power disruption is common.
Read more: http://www.roadtrucker.com/engel/engel-12-volt-fridge-freezer-technical.html#ixzz2MvRL2xrC

i need a schematic diagram of a fridge

if compressor is running, then you are correct in saying no point in replacing stat. by sounds of it you have a faulty compressor fault or a syatem fault - impossible to dignose by remotely. this is not a diy job i'm afraid