The only time I have that happen is if I have empty fuel tanks with the crossflow Fuel Valves CLOSED. Half of the engines flame out. A restart is needed after opening the crossflow Fuel Valves.
Some advice - If you notice that the aircraft is slowing down and/or the Angle of Attack is getting higher, check your engine gauges, you are bound to see that one or more engines are no longer running!

Same for the 707. I have had it (half of the engines flaming out) happen a few times when I have not monitored the fuel tanks correctly. Once a fuel tank is empty, turn the Fuel Boost Pumps (for that tank) OFF and make sure that the Fuel Valves (crossflow) are OPEN. This doesn't apply to the reserve tank Fuel Valves, UNLESS they are the only ones with fuel (and you're in real trouble if that is the case!).

Mark