What does "ineligible week" mean?

Ineligible means they are not eligible for benefits for those weeks. A claimant would have received notice letting them know about the ineligibility.  

The reasons why vary and could include issues from failure to timely certify without good cause, to wages earned greater than 1.5 times their weekly benefit amount. If the matter holding the claimant not eligible is resolved, the certification status is modified. Once modified, if nothing else is preventing payment, eligible funds are released.

In all situations, a determination is issued, and the claimant has the right to protest. 

To submit your protest/appeal in MiWAM, click on the blue 'File Protest/Appeal' link on the far right and type an explanation of the reason(s) why you disagree with the decision. To protect your rights to benefits during the protest period, please continue to certify biweekly through MiWAM online or MARVIN by phone during your scheduled certification week until you have returned to full-time work.