A prolonged argument or disagreement. When those two are in a running battle, it's hard to get them to finally reconcile.
a running battle
COMMON A running battle with someone is an argument or fight that you have over a long period of time. The government's running battle with the media took a significant new turn yesterday. Note: You can also say that someone has or fights a running battle with or against someone. `For the last four years I've fought a running battle against vandals and thieves,' Mr Hearsum said.
a running battlea confrontation that has gone on for a long time.
Literally, a running battle is one that is constantly changing its location, the opposite of a pitched battle (see pitched). The expression running fight was used in the late 17th century to describe a naval engagement in which the fight was continued as one party retreated or fled. Running battle appears to have originated in the mid 20th century.
a running ˈbattlean argument, a dispute, etc. which continues over a long period of time: There’s been a running battle between John and his neighbour for years about their garden wall.
Running here means ‘continuing’.