Just cause for termination

Our business requires that an employee informs the office of unplanned absences at least 4 hours before his scheduled duty. This is to give enough time to find a replacement so as not to obstruct business operations. One employee always fails to inform the office of his absences and he has done this 5 times already. He has been given memos and he wrote an agreement that should he commit the same negligence, he shall not be given another chance. Should he commit another absence without giving proper notice, would this be a valid ground for termination?

Hoping for a clarification on this. Thanks!

in my opinion, no.

Ok, thanks! i thought this could be under gross neglect of duty. What should our next step be, should this behavior continue? Thanks again.

there will be those that will disagree with me, but I am of the opinion that it doesn't fall under the degree of 'gross', but maybe serve him a suspension first if he does it again and termination if it reaches 10 times in 6 months

Thanks for the reply. New question: is it still ok to reprimand a violation which was committed about 6 months ago? Or will there be no bearing anymore considering the lapse in disciplinary action?