Any unit within 12" of the Battle Standard may retake a failed. The unit is only allowed to retake any Break test once, a re-roll may never be re-rolled.
If the General is within 12" of the unit as well then it will also benefit from being able to use his Leadership value. These two factors combined, the General's Leadership and the opportunity to re-take a failed throw, mean that units near to the General and the Battle Standard will tend to hold their ground come what may.
A Battle Standard only allows a unit to retake a failed Break test. It doesn't entitle a unit to retake any other, such as a or a test to . This rule ceases to apply if the Battle Standard is fleeing.