If your trailer doesn't have a battery disconnect switch, either stock or after-market, the most likely culprit is going to be the fuse for the battery's hot wire. Somewhere on the hot wire, you'll find a fuse, either glass or the AGM style (plastic with blades for contacts). With no disconnect switch (and I believe that Cruiser is correct, the '06s didn't have them), the fuse would be the only problem I can see as causing the symptoms you describe. Do your other 12v items work, i.e., the fan, the refrigerator (on LP), etc., when hooked to shore power?
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)