Whether or not the anime will be renewed for a second season depends on several factors, including the series' popularity, sales, and production costs.
In terms of popularity, Skip Beat! has a dedicated fan base and has received generally positive reviews from viewers and critics.
However, in terms of sales, the anime's DVD and Blu-ray releases in Japan have only had modest sales figures, according to Oricon charts.
There aren't any announcements from the official sources about season 2 coming out anytime soon as well.
Ultimately, the decision of whether or not to produce a second season of Skip Beat! lies with the production committee, consisting of various companies and individuals involved in the production of the anime.
If there is enough demand from fans and the financial returns justify the investment, a second season could be greenlit in the future.
I recommend staying up-to-date with official sources, such as the Skip Beat! anime's official website, social media channels, or reputable anime news sources, for any announcements regarding a potential second season.