Mario,
I know we are talking in the "electrical bay", but your originally described conditions of power loss and stalling sounds more like a possible fuel starvation/restriction problem. Possibly rust/debris floating around in the tank till suctions draws it to cause a feed blockage (or in an inline filter possibly). I think the ability of the engine to restart after sitting a while may indicate that if you have a debris blockage, it could be settling out to allow fuel to flow until the debris is stirred up again and blocks off the flow again. A lack of fuel would account for the reduced idle speed/power loss and eventual stall out and the reductions in generator output could be related to just the reduced engine RPM.
Just a little out-loud thinking and maybe worth you checking out to eliminate this as a possible problems source.
If replacing your regulator doesn't resolve the issue, check your fuel circuit.
Dan
