The issues reported at #5569 seem to stem from situations in which units end up stuck having failed 3 paths, and never actually 'failing' when computing further long paths. So they end up stuck permanently in this 'I need to compute a long path now' state.
The reason for that is from the POV of 'PathResult', the long paths computed are legitimate: they get the unit in-range.
However the unit cannot move at all since it's immediately obstructed by other units nearby. So it never ends up incrementing the failed paths counter, nor resetting it.
This isn't really solvable while we keep the multiple pathfinder systems, so to avoid this I'll just increment the counter when computing a long path in this special state, which means that units can never be stuck in it.
I guess that happened more often in MP games because turn lengths are longer, thus more opportunity to be stuck.