SP20 & ROG, Hi. Most modern braking systems are power assisted, as is generally required by disc brakes which have a higher clamping force requirement. This assistance comes from a vacuum booster which draws vacuum from the intake manifold. When the engine is not running, manifold vacuum is lost and hence breaking effect is lost. Often there will be some residual assistance after the engine ceases operation, but the residual vacuum in the booster diaphragm housing gradually decays until you have no further assistance. Therefore, if it happens again, use your residual vacuum assistance wisely as it is a finite resource. You will still stop with no vacuum/booster assistance but it will require much more pedal effort than you are used to. Knowing this will prepare you for it and you shouldn't panic if you feel the car is not stopping at all. Just allow more braking distance until your main issue is resolved.
It will help us to know if your engine stoppages are a series of hesitations and/or progressive loss of power or a sudden stone dead cut-out.
If the former it is either fuel starvation or fuel exhaustion (your description of "stumbling and chugging" might point to fuel issues though the latter option of exhaustion seems less likely or unlikely in your case). Blocked fuel filter(s), sucking air though a cracked line or crook union, or a defective pump can give rise to intermittent starvation.
If the latter (sudden stoppage), it is almost certainly electronic or electrical (there IS a difference). I'm betting in that case that if it isn't a crook ECU then the problem is a simple intermittent electrical connection issue, even a bad earth, but given limited info and no physical inspection, I'm prepared to stand corrected.
I don't know the SP20 intimately, but a bit of net research shows it to be a 2 litre twin cam four cylinder with fuel injection. Can you fit a Dashhawk (or similar) that might give you an error code?
CP_e Standback & PNP; CP_e 3" SS Downpipe; Corksport FMIC with Top-mount K&N filter & OEM Ram CAI; Turbosmart BOV; Dashhawk; Prosport Boost Guage; JBR solid shift bushes; DBA 4000 Wiper-Slot front rotors; Hawk Ferro-Carbon HPS Street front brake pads (@ 69,000km); Sumitomo HTRZIII's in 225/45 x 18