Honda EU 1000 generator question

Hello all, new member here. I have a question about my Honda EU 1000. It is a small thousand watt gasoline powered generator. I bought this to charge my Electric bike batteries while camping. And it works fine for that. I had what I thought was a great idea to put the generator in my bicycle trailer and charge the batteries while biking. What I found out is the generator does not want to run properly while in motion. Wants to surge up and down quite a bit and even stopped running a time or two during the testing that I did. Maybe this is a bit dangerous or perhaps way more dangerous than I realize. Can anybody tell me what is going on? Like I said the generator works fine when stationary. Thanks for any help or advice.