i would say it would weaken it but not undo it. a circle creates holy ground and protection against negativity. if the circle is broken, it weakens the energy is the area you are casting, but if you ignore it and continue the spell, it should still work, it just wouldn't be as strong.
if you stop, close the circle, and continue casting, i would say your spell would fail because you broke your concentration. i would start from the beginning if you chose to recast the circle.
if someone out of spite is deliberately breaking the circle, then go some place you can lock a door to keep them out. the one nice thing about circle than say a church, is if someones bothering you, you can move your holy ground wherever. much harder to move a building.