If the assignment is the Advanced uploading of files type, then once the student has pressed Send for Marking, he/she cannot resubmit. The teacher can hit the Revert to Draft button on the grading screen to allow the student to resubmit.
If you're using the Upload a single file type, there is an Allow resubmitting setting on the update assignment screen. If this is set to yes, the student should be able to resubmit.
If you're using the Upload a single file type, there is an Allow resubmitting setting on the update assignment screen. If this is set to yes, the student should be able to resubmit.