The phrase "a challenging month" is correct and usable in written English.
You can use it to describe a month that presented difficulties or obstacles, whether personally, professionally, or in other contexts.
Example: "Last month was a challenging month for our team as we faced several unexpected setbacks in the project."
Alternatives: "a tough month" or "a difficult month".
A VW executive called April "a challenging month," but said the company remained focused on its long-term growth strategy.
David Martin, of the Scottish Retail Consortium, said: "September was a challenging month for retailers with a combination of factors contributing to the weakest sales performance since January 1999, excluding Easter distortions.
"January has always been a challenging month," said John Lynch, chairman of the Jamaica Tourist Board.
It has been a challenging month for the Vita, which has sold around ten million units since its launch in February 2012.
Management said that February was a challenging month that materially impacted sales comps, but they believe that results for the month were more of an outlier than a norm.
This has been a challenging month for Nadal.
Now Damon is trying to energize the Yankees, trying to get them through a challenging September and into October.
One point of caution: the FPI rates Michigan State's schedule as the 24th-toughest slate in the FBS, including a challenging October that features home dates with Northwestern, Michigan and Purdue and a road game at Penn State.
It was a busy and challenging month, but the faculty still found time to teach, and the residents made me really feel part of the team.
"It's been the most challenging month in the 27 years I've been a climatologist," says Neil Plummer, assistant director of the Climate Information Service at the Australian Bureau of Meteorology in Melbourne.
Philadelphia had won 10 straight at Lincoln Financial Field before their last two defeats, and in this historically challenging month for Romo's 'Boys they showed that this particular team may be a class above previous failures.
