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.
Assignment
Resubmission of a single document
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