According to Business Insider, a member of Apple discussion forums has been informed that Apple will be ending to promotion as of 2015. The promotion has been running since 2004, so it is strange that Apple would end it now.
Via Apple discussion forum user Bob Foss:
I contacted iTunes Support and they told me the decision was made to drop the free Single of the Week. Seems they don't want people browsing the Store anymore. I told them that the free single each week got me to the Store and I usually bought a few songs. Now, there's less reason to go. They've stopped the free single in other countries too.
Apple has recently ended its annual "12 Days of Christmas" iTunes Store giveaway, so could it be that the company is getting greedier than ever, or are the promotions not financially viable anymore? Foss' confirmation has yet to be verified, although we haven't seen any iTunes "Single of the Week" tracks in 2015 at the time of this posting.