The short answer
A video doorbell reporting low power means the transformer can't feed it enough juice. Not enough voltage, not enough wattage, or both.
Modern camera doorbells are hungry. They want 16 to 24 volts AC and 10 VA at minimum, and they draw a real surge every time the camera wakes up to record.
Older homes came with transformers built for a simple ding-dong chime. Those often put out 8 to 10 volts at 5 VA, which was plenty in 1985 and nowhere near enough now.
So before you assume the doorbell is defective, go find the transformer and read what's printed on it. That one label answers the question most of the time.
What's actually causing it
There's a short list of suspects here, and they're easy to rank.
First and most common: the transformer is just too small. A 5 or 10 VA unit can't run a camera. This is the answer in the majority of older homes.
Second: voltage drop. Doorbell wire is thin, usually 18 or 20 gauge, and a long run from the transformer to the door bleeds off voltage. Add a corroded splice and you lose even more.
Third: bad connections. Terminals at the button sit outside year-round. Green corrosion and loose screws add resistance and choke the current.
Fourth: the chime. If you have a mechanical bell, the doorbell maker's diode or power kit needs to be installed correctly, or the coil drags voltage down.
The transformer itself failing is real but less common. They're simple devices, but 20-plus years of heat can drift the output low or partially short the windings.