Hi, Willem,
I think it is a wrong concept that the waking-up event follows up the Reset procedure. As you know that waking-up event from sleep/deep sleep/power-down modes follows up the interrupt process, in other words, assume that the LPC processor is in above low-power mode, when the waking-up event occurs, an interrupt is triggered, the corresponding ISR is executed, after the ISR is finished, the LPC CPU will resume to main loop where it enters the low power mode.
In deep power-down mode, the waking-up event follows up Reset process.
Because the waking-up follows up interrupt process and in power-down mode, maybe the ADC is power-down, so it is necessary to initialize the ADC and clock module in the main or ISR. I suggest you initialize the ADC in the waking-up ISR for simplicity, pls have a try.
Hope it can help you
BR
Xiangjun Rong