My elderly cat (16yo) has been wanting food literally all the time. I feed him and a few minutes later he is crying for food. He has been going through six packs of wet food every day (he has refused dry food for the past six months).
I took him to the vet today worried it might be his thyroid. She said he is in really good condition for his age, his coat is lovely, his teeth are fine, basically everything is in tip-top shape (except for his cataracts and arthritis which we already knew about). But he is going senile. When we feed him, he eats and then forgets about it and thinks it is his dinner time again. 
We have been a bit stern with him when he cries for food right after he's eaten, thinking he is just being greedy. I feel awful. 
The vet said to buy senior pouches, and feed him a little bit whenever he wants food.
Mind you, him being a bit wrong in the head means he does fit in well with this family 