If it's doing it after the stove is hot, sounds like somethings plugged in the main line. I have a old Hillrange pressurized alcohol stove and love it. I posted a thread here on how I recently serviced it. Search if interested.I lived with several Kenyon stoves over the years. The issue you describe is common. A couple of things to check. Make sure the pump is working well and you have pumped the tank up properly. Next, don't shortchange the preheat process. If not preheated properly it will surge as you describe. Try taking the burners apart and cleaning thoroughly including replacing the filters. No guarantee after you go all this the stove will operate properly. They are very touchy.
When the budget allows, get an Origo.