New Do you mean that the PCI-E connector couldn't cope with an extra 39W ?
No, I was thinking of power delivery to the GPU chip itself:
To turn 12V supply to the 1.X-ish V the chip itself uses, the card has a DC-DC converter on-board. Because the chip needs a very smooth (no variations) power delivery, it uses a 'multi phase' design: each DC-DC converter will 'pulse' its power delivery, as it uses an oscillator as part of its design for efficient conversion, so by using multiple phases those pulses can be smoothed out along with the aid of capacitors. e.g. in a '6 phase' design there would be 6 separate DC-DC stepdown converters, each 'peaking' their delivery one after the other (the oscillations are 'phase offset'). When all phases are providing the same proportion of the power, this works fine. When one or more phases are not, there is now the possibility of a 'dip' in available power.
Now, variations in phase power is expected and GPU (and CPU, located on the motherboard) power conversion circuitry is designed to compensate for this. This is why there are capacitors on the board: they smooth the power delivery by 'buffering' the power (to greatly simplify things). Where a problem could occur is if the amount of power the capacitors have been specced to be able to 'buffer' is sufficient to handle one phase suddenly supplying 1/4 of what it was designed to do. If it can, you're living on the edge of stability but the card should still work. If it can't then, dropping the PCIe slot power draw that far may result in instability as power delivery is no longer smooth and always available.
Because this is dependant on how the power delivery circuitry on the card itself was designed, this is not really something that can be determined beforehand.