Trailer battery

My travel trailer battery continues to go dead and will not charge when hooked to shore power. It is a new battery. The output from the trailer to the battery is a "pulsating" 12v.
It also apparently charges while hooked to my truck.
I used the trailer over the weekend, connected to shore power but when I disconnected the trailer the battery was completely dead. Once hooked to the truck everything was fine again.
What is going on?

Hello Bob, welcome to the forum

This is a very strange problem, I will try to find out what it can be. But I honestly cannot see how hooked on to the truck the trailer provides different output as unhooked

when your unit is plugged into shore power, the ac power from the plug runs into an inverter which turns the power into dc wich in turn powers all your 12vdc lights etc as well as charging your trailer bat.
I would first check for something obvious blown fuse at the inverter, loose connection etc. I do not recommend removing the inverter cover unless you are electrically inclined. due to the possibility of shock

when the unit is plugged to your truck, the harness has a "charge line" or wire that runs to the battery, thus charging from you truck alt.

Thanks for the response. I walked back through everything. I did pull my power panel as I felt comfortable doing it. I also looked for the proverbial in-line fuse but could not find one. I rechecked my voltage readings and recharged the battery with another charger. After my battery was at full charge I was getting about 12.70 off the battery. I was getting about the same reading coming off the lines to the battery. I reconnected the lines to the battery and got a "full" reading on the trailer indicator (without shore power). I plugged the trailer back into shore. After about a week I rechecked again. Battery at 12.70 as well as lines to battery. Trailer indicator now at 2/3 power (without shore power).
My thoughts (needing feedback): When I bought the battery I assumed it was fully charged. Perhaps it wasn't and trailer only maintained what was in existence. Also I don't think trailer indicator is as accurate as a meter.