However, in 2013, both Kvapil and BK Racing struggled. Kvapil dropped to 31st in points, recording five Top 20 finishes but nine DNFs (including five blown engines). The team released Kvapil shortly before the start of the 2014 season.
On October 8, 2013, Kvapil was arrested by the Mooresville police department following a domestic dispute. Kvapil was charged with assault on a female and false imprisonment, and was released on $1,000 bail. Kvapil was allowed to race in that weekend's Bank of America 500 at Charlotte Motor Speedway. On January 30, 2014, it was announced that Kvapil had accepted a plea deal in the case, pleading guilty in exchange for having the case dismissed following two years' probation, community service, and attending an anger management class.