12v power inverter problem

[airshot]

I have a 12v plug in the cigarette lighter inverter that I use to power a small boom box radio on my boat. In fact I have two, one is used for my aerator on my minnow bucket. Tye problem is they stopped working on my boat. When I plug them into the car they work fine but not the boat, the little fan runs but no power for the radio off either one of the inverters. My plug in spotlight works fine in the lighter plugs but not the inverters. Not sure what is going on here but thought I might throw this out there for some of our experienced electronics people. I am a toolmaker by trade and have just a basic understanding of electricity but this has me puzzled. Radio works fine when plugged into 120v and works fine when inverter is plugged into car but not the boat......yet my other 12v items work fine on the boat. Been using this for the past two years without a problem but this year no radio.........

 

[NYBo]

WAG: The voltage at the socket is below the critical level for the inverters so they won't provide any output. Check for corrosion at all the wiring connections, and inside the socket itself. Maybe the fuse is corroded? Are you sure the battery is fully charged?

 

[airshot]

Well I feel pretty dumb.....as I have twin batts on board, dummy me checks the wrong batt which shows full volts. Then I came to realize I should be checking the deep cycle accessory batt which was low. After charging overnight , then letting set for 24 hrs and rechecking I have found some bad cells so this is all making sense. Time to replace the accessory battery, even though I can't complain it is a little over 5 yrs old.
NYBo.....thanks for the information on the inverters, did not realize that the voltage drop would shut them off, funny thing is the little fans inside the inverters still ran even though the inverter did not put out voltage, making me assume they were working.