The last dance is on the horizon for the Broadway outpost of “Billy Elliot,” which has set a closing date of Jan. 8.“Billy” swept the 2009 Tonys, recouped its $18 million capitalization in about 14 months and until this year, consistently logged weekly sales of $1 million or more. Still, the tuner couldn’t manage the longevity of hit U.K. imports such as the 10-year-old “Mamma Mia!” Weekly tallies from recent frames haven’t been spectacular, but they were far from dire, aside from the clobberings “Billy” took from Hurricane Irene and from the traditional post-Labor Day drop. Last couple of seshes saw the show pull in around $720,000 per week. Maintaining “Billy,” however, is usually a pricey endeavor due to the constant need for triple-threat young thesps who swiftly outgrow the role of the protag, a coal miner’s son from northern England who just wants to dance. The producing model therefore includes a kind of wunderkind factory that constantly scouts, trains and rehearses young performers. It’s an unusual cost for a Broadway show to bear. Some in the industry also speculate that the specificity of the show’s social and political backdrop (set during a time of labor unrest in 1980s England), along with the plentiful cursing from everyone onstage, has kept the tuner from achieving longstanding success with American family and tourist auds. Still, Broadway’s “Billy” has generated plenty of coin in its time on the Rialto, with the tuner ringing more than $170 million since it began perfs Oct. 1, 2008. “Billy,” with book and lyrics by screenwriter Lee Hall and music by Elton John, had its world preem in London in 2005, where the Stephen Daldry-helmed staging is still playing. There’s also a North American touring production out on the road. The Broadway incarnation is produced by Universal Pictures Stage Prods., Working Title Films and Old Vic Prods. in association with Weinstein Live Entertainment.