Multiple possible causes but to answer the subject: YES.
First: As the A/C ages it may need a bit more "Kick" to start. A Soft Start kit MIGHT fix this, also general preventive maintenance. (Cleaning and such, specifically fans, blowers and condenser coils)
Also check all screws on Circuit breakers, and wires to make sure they are tight, Many RVers have .. A few screws loose.
Next your 12 volt side of life.. As we plug in more and more devices the power load caused by the converter increases.. Poor batteries may add to that as well.
Finally we have the generator itself. Spark plugs foul, Carb's gum up, and other issues which you might not notice at half load, but when that big compressor kicks in and sucks up the power.. YOU NOTICE. The engine no longer has what it takes.. Given your description, That's where I'd start.