The phrase "a rough couple of weeks" means that someone has experienced a difficult or challenging period of time, typically two weeks. Full definition
For those who believe in the dignity and value of gay and lesbian people and who support LGBT equality both in the U.S. and abroad, it's been a rough couple of weeks. (rachelheldevans.com)
After a rough couple of weeks to start the Summer (vs. Team Maione and Team Foreman) they have rebounded nicely and are now back to.500. (allsportsseries.com)