The real problem here is the possibility of too low of a voltage at your camper to start your air conditioner compressor.
If you are running your A/C while at home, the voltage at the outlet the camper is plugged into is probably pretty good - at least 115 volts, possibly a bit higher. The voltage drop across a 100 foot 14 AWG extension cord carrying 8 amps is about 4 volts. At home this is no big deal, as you still have about 110 volts at the camper.
If you try to run your A/C in a campground where you start with the voltage at the outlet is around 110 volts (or maybe even less...), you end up with 106 volts running your air conditioner - not a very good situation.
This is one reason why it is important to monitor the voltage being supplied to your camper.
If an 8 amp load causes your extension cord to become warm, throw it away. It is probably a 16 or 18 AWG extension cord, which most certainly is not adequate for the job.
And finally, don't do as someone suggested above and turn on your A/C within a minute or two of shutting it off. The pressures in the compressor will be much too high to allow it to start, no matter what size or length extension cord you are using. What happens when this is tried is you trip the overheat protection in the compressor motor, resulting in no cooling until the compressor cools off. This usually takes longer than it takes for pressures to equalize, and when the compressor cools it resumes normal operation.
-- Dan Meyer