Hi. My name is***** Thank you for your question about Paco. Do you feel that the 1 day he's not eating is also the day that he vomits? Is he vomiting on the days that he's eating well? Is he losing weight?
To put things in perspective here, the days he's not eating is most likely tied into why he's having the random vomits. The fact that he's vomiting randomly means his stomach is upset and due to that he's not wanting to eat till it settle down. It isn't surprising that after a vomit, he's not having a good appetite. Why then is he having the random vomits? It could still be a food intolerance. You may just not have found the food that agrees with him the best. Sometimes this can take a couple different dietary food trials to find the diet that is best for him. This would be a very simple thing to continue to explore. You could try another brand of food's dietary sensitive diet and give that a month or so to see how it helps. Could the random vomits be due to him finding something outside and eating it? Plants growing outside are honestly the most common reason for the random vomits when a cat gets outside. I can count it like clockwork when my older female slips outside due to one of the kids leaving a screen door open. She runs out, eats some grass (why??? who knows) and then about 2 hours later, she'll start to feel punky and vomit and then turn around in about 8 hours.
Hair balls could also do something similar too. What you could do to maybe help eliminate that from the equation if it is an issue is to brush him every couple days. Brushing him on a regular basis will drastically reduce the fur ingested that could coalesce into a hair ball.