We have a 96 rexhall rv. we have had the unit plugged into shore power from the house and had been running the air conditioner. it ran great about 4 times and now we can not get it to kick on with just the shore power, but on the generator it works great. what do you think is wrong? thank you.

If your plugged in to a 15 amp household receptacle, then an extension cable of any kind or length, then that is likely your problem. An AC unit should have 20 amps of good power available to it. If your using an extension cord of any kind, and it is any less than 12 gauge wire, then that will cause a drop in voltage as well. Obviously the best scenario would be to install and wire a 30 amp receptacle outside your house just for that use, if done often. Take a voltage reading at receptacle, then inside RV, and see how it is probably a little less without even the AC on, then when AC kicks in, or tries to.
It may work once in a while, but it's not good for the AC to try and operate on low voltage, which causes a higher amperage draw.