I don't quite understand it - the manga is popular, ongoing and their are plenty of fans, and yet - from what I've researched - there was never a North American licence and never an English dub.
Why was there never a Skip Beat dub?
The anime of Skip Beat was in 2008/09 , by Hal Film Maker. Shortly after the anime, Hal Film Maker merged into the parent company TYO Animations. There may have been some issues with licensing works from a company that didn't exist anymore.
This was also around the time of legal online streaming's emergence - so interested studios (possibly Funimation, who took on B Gata H Kei - Hal Studio's next production) had a lot of business decisions and work at this time.
Most dubbed anime go under a lot of cost analysis to see whether it is worth it to produce. Usually shounen works are the easiest of works to pull a profit on. Shoujo works are harder to sell, so perhaps it was decided by most companies that it just wasn't worth it.
Any of these could be potential reasons and this probably isn't a very satisfying answer, but unless there's an official announcement by a involved company, we won't know due to company secrecies.
The longer it remains unlicensed however, the less likely it is to be picked up as it slowly looses the target audience's interest.
One reason there was never a dub for Skip Beat is the industry at the time truly believed only magical girl shoujo made money. Even now (2016) when some companies are adding more shoujo titles to their catalogs, they are still more hesitant to invest in shoujo at the same rate they invest in shounen, and the titles to appeal to girls/women licensed lean towards reverse harem, its cousin the newer bishounen subgenre, and yaoi.
Good news, though. More companies are crowdfunding left-behind licenses, and Pied Piper, the company that rescued and released Time of Eve, is running a Kickstarter for a North American release of Skip Beat. The disc will have the original Japanese audio, with improved subtitles, and a new English dub. The campaign ends April 16, 2016. http://kck.st/1RooUS7
I began this as a comment on Toshinou Kyouko's answer, and it's sort of a supplement to that answer.
US companies, in general, have become a lot more averse to producing dubs. In the days of Geneon (2003–2007), almost everything that came out had a dub. That is no longer the case; lots of shows come out with no dub, and it seems that, as Toshinou-san mentioned, any show that isn't going to make the sales doesn't get one. Shoujo anime typically doesn't sell that well in the US; only a small fraction of all the shoujo produced even comes out here. (Shoujo manga used to sell well, in the age of Geneon, which was also the age of Tokyopop.)
Why don't companies want to produce dubs? The economics of anime has changed pretty drastically. In the Geneon days, you bought anime as a series of DVD releases, usually six or seven of them, for about $30 each. That works out to about $180 to own a complete series, but the companies also sold a lot of individual copies of the first few discs. (If you think that's bad, the original release of Eva was on 13 VHS tapes, each with two episodes, and you had to pick whether to buy the dub tapes or the sub tapes.)
Legal streaming sites changed that. Whether you intend to buy the DVDs or not, it makes sense to watch it for free online so you know you're getting a good value. Everyone stopped paying $60 just to watch the first five or six episodes of a series to find out if it was good or not. DVD releases now are usually in box sets that contain 13 episodes. The US distributors have to assume that everyone who buys the DVDs has already seen the series online, which drastically limits the market for most shows. Also, US distributors today have seen Geneon and ADV fold because they spent too much money on fancy dub scripts and pop-up notes for shows that turned out to be unpopular. For shows like, well, about 80% of what I watch, producing a dub is a losing proposition.
I also believe dubs became less popular because the TV market for anime dried up. In the mid-2000s, TV networks were hooking up left and right with anime distributors. Cartoon Network was working with Viz and Funimation; Encore was carrying titles for ADV and Media Blasters; Geneon worked with TechTV (later G4) and even had a deal with MTV that resulted in a disastrous run of Heat Guy J. As far as I can tell, no one except Cartoon Network is carrying anime anymore, and they've scaled back quite a bit. The networks have also been hit by the Internet, and they've figured out that they can produce their own anime-like content, such as Avatar: The Last Airbender, and have full control over it, instead of having to work out some weird limited-term licensing deal with a US distributor who already has a weird limited-term licensing deal with a Japanese distributor.
Producing a dub is much more expensive than producing a subtitled translation; that's why you see lots of fansubs, but very few fandubs. That's also why streaming sites such as Crunchyroll don't produce their own dubs. And since anime is still fairly low-profile in the US, for a lot of shows, it just doesn't make sense to spend that money.