1. No power reaching it
A GFCI needs power to latch. Check the breaker (a tripped breaker sits between ON and OFF; push it fully off, then on), then any other GFCI upstream — the dead outlet in a bathroom is often fed from a protected one in another bathroom or the garage. On a portable device, check the outlet with a lamp.
2. A fault still present
The device resets and trips again, or refuses while a load is connected. Unplug everything downstream and try again. If it holds, plug things back one at a time; the one that trips it is the fault (a heater element, a wet extension cord, a tool with a cracked case). If it still refuses with nothing plugged in, the fault is in the wiring downstream: disconnect the LOAD conductors (power off) and retry — if it now holds, read trips with nothing plugged in.
3. Line and load reversed
A receptacle GFCI made after 2006 will not power up or reset when the feed is on the LOAD terminals. New installation, new device that never worked: this is it (line vs load).
4. End of life
A self-test device that has failed its own check locks out and shows its fault indication; an older device simply dies. Either way RESET will not hold with power present and nothing connected. Replace it — it is a $15–25 part — and consider a self-test model (why).
Portable devices
A manual-reset plug head or in-line GFCI is designed not to reset after a power cut until you press the button; that is the feature, not a fault (manual vs automatic). If it will not hold with the tool unplugged and the outlet live, the device has failed the test and comes off the job.