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As stated above, charge the battery (leave it on shore power), pull it, take it to Autozone and they'll tell you what kind of shape it's in. Full discharges are really hard on batteries and it won't take long to kill it.
The other thing that you could do is hook up a 12V amp meter between your battery and trailer to see what you're drawing with all systems off in terms of amps. Any automotive-inclined friend or neighbor would likely have a meter with an amp function.
For comparison, my trailer draws:
1) 1.4 Amps with everything in the OFF position. (I didn't try with the fridge on)
2) 0.04 Amps with the battery disconnect in the disconnect position (things like C02 detector continue to stay hooked up)
A group 27 battery is typically rated to 90 amp hours... IE - several day minimum with nothing running. Either you've got a high parasitic drain somewhere or a weak battery.. Maybe both.
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