12v cooler killing battery?

Ok I have been OTR for a year now and havery had 3 different 12v coolers (1 dies buy another). Never had a problem leaving them plugged into the 12v socket when the truck was turned off over night. This morning woke up, the cooler wasn't running and my batteries were down to 12v and the truck wouldn't start. Got a jump start and truck is running ok, but my office is saying its the cooler that drained the battery and shouldn't be plugged in without the engine running. It was my understanding that the truck wouldn't let the voltage drop to low to keep the truck from starting but I guess not.... So do you all have this issue and how do you deal with it? Can't afford to eat expensive crappy truck stop food all of the time and often stopped in rest areas where the cuisine is nothing more than chips and candy bars.

 

I didn't mean the cooler having a low voltage cuttoff but the truck itself. It's possible that one or more of the batteries are bad but the company won't test or replace them if the truck starts. Rather wait for a situation to happen and cause a load to be late than be proactive.

 

Cool it's nice and quiet out there

 

That's a long wagon ride to town

 

I agree I don't think the cooler caused the problem, but that is what they are blaming it on... Total bs in my opinion but so be it. I will be doing this job to some degree for quite a long time but just won't be with this company, there are other options available with more perks.