Does the water heater produce radiant heat to the exterior of the unit

Where is this copper pipe located and what type of tank are you working on? If you had baseboard heating and replaced a section of copper with regular pipe, there would be a substantial drop in radiant heat. Is this what you are talking about or is there no heat being produced at all? Please take a look at the repair area and see if there was some part left off or hanging. Its possible a safety parameter has not been met and isn't allowing the heater to turn on. If you have more information please feel free to write back.

I just looked on the website which contains a remark there is only approval for installations for campervans and caravans.

Nowhere in the description or specifications does it mention a flue or ventilation requirement which is very surprising because burning gas needs a good supply of fresh air and produces poisonous gases that must be got rid of/vented to the exterior.

I guess you could use your heater as long as the requirements of an adequate fresh air supply and the venting of combustion gases is taken care of...

if you leave the heating on low to stop freezing is fine . Not sure how you water works but I would leave it on to stop freezing Also get some one to pop in once a week to check things are ok .

If you have tankless electric, it can simply be insulated... but tankless electric are seldom mounted outdoor.
Service bulletin says: "the only way of assuring protection is to completely remove the heater during those times the area may experience freezing temperatures.

There are tankless with built-in heater for exterior installation.
Check your manual, or add a comment with specific model number and maybe I can find the information.

Here's why they install tankless outdoors: Because tankless burn more fuel per gallon of hot water. This requires larger gas line and larger vent pipe than typical tank-type gas water heater that is usually installed indoors.
They install tankless outdoors, so there is no need for expensive vent pipe, and because there is ample incoming air to support combustion.
So if tankless does not have factory-installed internal heater, then the unit can freeze easily when the combustion draws in cold air.
Of course you can put heat-tapes on the pipes but the heat exchanger inside will quickly freeze during periods when hot water is not being used, and combustion is not taking place.

You can move the tankless installation inside and use correctly-sized vent and intake pipes directly through the wall. This will generally protect tanklesss from freezing if room is heated adequately.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

You're probably in for a service call and/or possibly water heater replacement if unit is more that 5-6 years old.
Your water heater plugs into outlet. Check outlet with cheap circuit analyzer to make sure the unit is receiving correct polarity without line interference.
If unit is in the attic, then add more venting to soffit and roof so pilot is not being snuffed out by hot air. If unit is in basement, then open some doors and a window and see if unit needs more air.
Most gas water heaters require yearly cleaning and service.
Clean the combustion parts and tubes.
Clean the air intake.
Have gas company check gas pressure.
Open following link for possible illustrations:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

The problem can be bad gas control valve, air in gas line, low gas pressure, gas shut off handle not fully parallel with gas line, dirty combustion parts, lack of combustion air, improper venting. Or combination of all things. It's an electronic gizmo, anything can be bad or shorted, and repair may not last long.

Without a trained service technician to ohm-test the parts using correct service manual, then we are guessing at the cause.

Power vent water heater implies that you have side wall venting which must be replaced with another side-wall vented unit -or- it implies rapid reheating of water.

If water heater is more than 6 years old, you might be money ahead by installing a new one from local box store. Avoid the power vent and electronics. Local box store will have passive roof-venting type water heater BUT box store does not sell side-wall power vent. If your power vent goes up through the roof, then box-store variety gas water heater will work. Total cost $350 do-it-yourself for 40 gallon gas.
Or get 40 gallon 240Volt electric for $220 and connect to circuit breaker box. Requires no venting, and is easy to repair for years to come.
Or small 120Volt electric that plugs into outlet to tide you over until gas repairs can be made.
Look for scratch-n-dent models and always offer 10% off.
http://waterheatertimer.org/How-to-install-gas-water-heater.html
Shower uses 5-9 gallons hot water.

This model is known to have problems with its Thermal Cutout this regulates the maximum water temp and can cause the unit to overheat when it does not shut off the heat source. In some residences low water flow and or a obstruction (common if you have well water) in the filtration and water treatment system can cause the same problem. Basically the unit can have overheating problems and the heat exchange coils are be prone the effects of hard water (if that applies to your water supply) and can lead to future service of descaling the units coil/coils (can be expensive). Buying any used unit with many mechanical parts and other components always have the potential to have problems new so i would not recommend a used unit of this type.

Also, This unit is limited due to the fact that the unit require­­­ incoming water to be cold and you cant use any sources of pre heated water (many people are starting to utilize alternative energies such as solar water heaters, wood boilers, and other relatively free or low cost). For example, using recovered heat from a boiler or indirect hot water tank or other to reduce the energy (cost) by raising the systems initial water temperature.

Are you heating a concrete floor with radiant heating? if so it would be far more cost effective to use either a loop off your existing system (a new zone) or you could add a oil fired or LP (gas) fired water heater and utilize the efficiency of a separate system and the fact that a hot water heater stores and super insulates the water it heats.

if you have any questions please feel free to let me know

I assume this is outside? A slow warm heat, would defrost it. If so, is there some way you can make a canopy of some sort to capture heat form say a portable heater of sorts? - Just encompass the tankless unit so it may defrost from the portable heat and you can see what is any damage has occurred and go from there..
Best regards
Ck

05 Imperfect Combustion Alarm
Clean air inlet filter.
Clean combustion air fan.
Clean heat exchanger fins.
Check for adequate combustion air ventilation openings and clean if necessary.
Check vent system for partial blockage and correct as necessary.

If this does not help; contact Rheem customer support.

The 2400ES in cold climates needs to be a twin piped unit. 3" SS venting with a combination air port made of pvc also 3 feet apart I believe on the same wall and at the same plane. Keep the cover on at all times and this will seal of the heater from the rest of the house and from freezing.

Is it radiant floor heating? I am assuming you're talking about the control unit... Need more information about the type of heater you're using, model, etc. Does it look like this?

http://www.stiebel-eltron-usa.com/radiant.html

If so, it's probably made by their sister company Energy Products.

http://www.energyproducts.biz

You can find the PDF for that heater which includes maintenance, installation, and troubleshooting information for their website.

http://www.energyproducts.biz/PDF/sharkmanual.pdf