The Unit requires a great deal of draft to heat that water.
Drill some large holes in the cover so the unit can get the right air to gas mix.When you work it with the cover off it can breathe. With it it on it cannot get the correct air/gas mix to make the thing work properly. MY best guess. Another thing is this when you cover it and the heat gets excessive withint the unit and it does brother! it probably shuts down a high limit to keep from melting that cheap cover. My opinion.