Once a person is saved, God does NOT "cut them off". That would require us to get saved all over again, and Jesus only saves us once. Not a million times. Otherwise his death at the cross would be a daily occurrence. Once you are saved, you're saved for life. Ain't no sin gonna change that.
For [it is] impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost, And have tasted the good word of God, and the powers of the world to come, If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put [him] to an open shame. For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: But that which beareth thorns and briers [is] rejected, and [is] nigh unto cursing; whose end [is] to be burned. Hebrews 6:4-8