There is no happily ever after.
I read romance for the happily ever after ending. I've always preferred romance series where there are different but related leads in each book because at the end of the book is that guarantee happily ever after. There is a conclusion to the story. We may see the characters again in the next book but the focus is now on a different couple. With an ongoing series with the same couple in every book, we don't get that happily ever after, only a happy for now until the next book.
There is usually a love triangle.
If there's one plot line I hate in romance, it's love triangles. I'm a traditionalist in that I prefer one hero and one heroine. None of that one hero and one almost hero and the heroine have to choose between the two, a plot line that's been really popular lately I've noticed (like in Jennifer Haymore's A Hint of Wicked--which is not an ongoing series but the only example I can think of and I book I haven't read so I can't make judgments). There can't be two heroes in mainstream romance--there's always going to be that "better" one you know the heroine is going to eventually end up with. Maybe it works sometimes but I just stay away from it because love triangles usually goes hand and hand with infidelity (whether physically or emotionally) and I can't stand reading about infidelity in any genre.
Unanswered questions that keep piling up.
An ongoing series can keep going on and on and on... After a while, the books become not so good anymore but you're still compelled to read the books because you want to know what will happen. You keep hoping that final conclusion will come and all your burning questions will be answered. But only a few unsatisfying ones are answered and you have more questions than before.
Other than Spider's Bite, I also won a book from a giveaway that is part of an ongoing series: Nalini Singh's Archangel's Kiss, the second book in her Guild Hunter series (but I won't read it until I get my hands on the first book). Jeaniene Frost's Night Huntress series, that I featured on my last "books I covet" post, is also an ongoing series. All these books I really want to read. I guess it's time I step out of my happily-ever-after box and try some happy-for-now books.