I would start by monitoring the voltage while running the AC. What kind of "shore power" are you plugged into -- home 15 amp outlet or 30 amp RV? Fan slowing down maybe an indicator that volts are sagging. If the voltage falls below 109 when running AC I would recommend turning AC off and finding another site with better power supply.
When I run my AC I monitor voltage using a Kill A Watt http://www.amazon.com/P3-International-P4460-Electricity-Monitor/dp/B000RGF29Q/ref=sr_1_2?ie=UTF8&qid=1403515563&sr=8-2&keywords=kill+watt+meter