Can Generator loose its power?

I have a Champion 3500-4000 Watt generator with a 30 amp plug that is about 4 years old. I have a 13.5 AC on my 2012 Keystone Springdale. I have run this AC before with this generator in the past. The last two times I tried to run the AC with the Generator it would kick on then start to sputter and sound horrendous. The generator has no problems running anything else in the trailer including coffee pot and Microwave and electric skillet. When I run the AC it was the only thing on. Same with microwave or coffee pot and skillet. Can the generator loose the electrical power it puts out? I was told by several that 3000 watts will run the AC. The AC ran fine at home on my 30 amp plug at my house both before and after this last trip.