If any spacecraft has remained at station-keeping with respect to the ISS for 12 hours or more, how far from the station did the craft remain?
The case of failed docking of Soyuz MS-14 may fit to constraints of the question. It was in orbit near ISS for 3 days between failed docking attempt and successful attempt. The linked above Wikipedia article states
the spacecraft backed away to a safe distance from the ISS
Further research resulted in locating few news articles mentioning that immediately after the first failed docking attempt the spacecraft was commanded to move away from ISS to "the safe distance of" (here sources vary)
whilst the decision was being made how to deal with the situation.
There's no further reports whether this distance was changed after decision was made to postpone docking for few days.
По расчетам баллистиков, в течение дня корабль будет находиться на безопасном расстоянии от станции...
According to calculations performed by "ballistic personnel" [sic] [perhaps meaning the personnel of "ballistic and navigation support service of Roscosmos' TsUP (MCC)], for the [next] day the ship will [remain to] be at a safe distance from the station
The first Orbital Cygnus mission that eventually docked with the ISS experienced GPS issues during its initial berthing procedure. The Cygnus aborted the berthing and retreated to a safe-ish distance from the ISS while Orbital engineers devised a software fix, initially planned for a two day delay. But then NASA asked Orbital for an even longer delay due to the upcoming arrival of Soyuz TMA-10M. Cygnus Orb-D1 berthed with the ISS a week after it initially arrived. In the interim, it retreated well behind the ISS, by a distance of up to 2400 km.
The tenth SpaceX Dragon mission that eventually docked with the ISS initially experienced a data error in its navigation system. The Dragon aborted its initial inberthing procedure and similarly retreated to a safe-ish distance. It then went into a racetrack pseudo-orbit about the ISS while SpaceX engineers devised a fix. This pseudo-orbit was much closer than was the Cygnus Orb-D1 retreat, about 7 km x 4 km, keeping the vehicle well outside of the 4x2x2 km approach ellipsoid. SpaceX CRS-10 berthed with the ISS a couple of days later.