G'day, there is such a feature.
It's under "favourite searches".
The downside is, if you put in a regularly occurring word or phrase, you get lots of hits: sometimes, far too many.
Secondly, you have to foresee how a seller will list the item you want, and search on those terms. Sellers who list poorly are inevitably overlooked. I've got some wonderful bargains when I've stumbled over poorly-described or misdescribed items.
The other drawback of E-bay's auto-search feature is that the emails that they send you are bulky, and they clog your inbox quickly. And, they only include 12 items per day, so if there are more than 12 new listings in a day, you still miss out.
In my experience, most items on
ebay are listed for auction periods of 7~10 days. So if you search once a week, you won't miss anything.
Peter in Oz