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I am sorry to learn of this situation.
If you can provide me with the jurisdiction that this occurred in (court where the petition was to be filed) I can give you a more definitive answer.
However, in general (almost all courts), filing dates for any type of appeal are "jurisdictional" - meaning that if you do not file an appeal or petition within the stated time, the court does not have jurisdiction to hear the issue (the court does not have jurisdiction to hear the appeal or discretion to change or bend the rules, regardless of the basis for the late filing).
What this means is that even though you may have a very legitimate reason for missing the filing date, there is nothing the court is going to be able to do for you, the underlying court opinion/judgment is going to be binding.
If your petition for review was for only part of your case, you may still be able to appeal the issue as part of a larger appeal at the end of your case, but the court is not going to be able to change the current ruling or order at this time.