His girlfriend and publicist, Jenny O'Brien (played by Gretchen Corbett), only appeared in "The Adventure of Colonel Nivin's Memoirs", an early episode (#8/23).
Ellery has a few girlfriends in the episodes. Each woman appeared in only one episode. This is consistent with the books. In some of the novels/short stories (at least the ones I've read), he'd be flirting with some woman, and we'd never hear from her again after that novel/short story. Usually it wasn't even made clear just how far the relationship went. The only regular character who was seen as his love interest was his assistant Nikki Porter (early 1940s), but in those short stories & radio plays, it seemed like she was more interested in him than he was in her.
There's a combination of 1940's morals and Ellery's portrayed distraction [does he have Asberger's?], some similarities to how Monk and Columbo are portrayed. Excluding "Mrs. Columbo", Columbo's wife is never seen, and her first name is never known.
It could also be that it would unnecessarily create a complication to the storyline that would not add anything - and leave him unavailable to those viewers who like to fantasize about him being available. Not that I'm aware of anyone fitting that description.
I don't think it really matters. He's a detective and his job is to solve crimes.
Dorothy Sayers put too much emphasis on her detective Lord Peter Wimsey getting together with Harriet Vane (whom he rescues from the gallows) and it was a very irritating distraction. It went on for five years and finally they married circa 1935. I remember reading that book....a painful read. They married. They had sex. I was really beginning to wonder if we'd ever get to read about the actual mystery.
I'm grateful to the authors who didn't put such an emphasis on this nonsense.
In most episodes, Ellery wasn't teamed up with any woman. I think he had a girlfriend in only about 4 or 5 episodes. A couple of those women were there to help solve the case. One of those women is in the short story (The Mad Tea Party), so she was kept in the TV adaptation.
Captain Kirk had a girlfriend in pretty much every episode, from what I remember. About 15 years since I've seen these episodes....