Kalispera Athina
one of the things about Alzheimer's is that those who have it often are active all of their waking hours. However much food they eat, they burn it off constantly by walking around, moving things, etc.
Also, you will find that most sufferers are on the thin side after Alzheimer's has taken hold. Whether that is due to constant exercise or the growing inability of their body to absorb food, I don't know.
If your mother is eating 3 meals a day but forgets that she has done so, it may be that she is purely working on habit, not hunger. Also, the need to eat is something so basic, we all remember it [there will be exceptions though] even when other memories have been lost.
Why not just give her something small to nibble - a bar of chocolate perhaps - and say that a meal is on the way.
It will do no good to tell her she has already eaten, and with her problems, some additional snacks will not cause any problems.
Best of luck!