Why would a cat go away and only come back after 3 to 4 days eat and go away again?

It's most probable your cat has more than one family in the area. All my cats over the years have equitably divided their time between various neighbours, who make a fuss of them. Eventually I get frantic and then the cat magically turns up, all innocent. Cats love the different foods and types of attention provided by their alternate families, but eventually they want the familiar old stuff at home. For a while. This is typical cat behaviour. Of course, if your cat is an undesexed she-cat, check her nipples in case she's had a litter somewhere. In that case you'll need to monitor her health.