Can a creditor ask the Bankruptcy Court to extend the time to object to my bankruptcy discharge?

Yes.

There is a strict time limit for creditors to object to the discharge of certain debts in bankruptcy, or to the discharge of all of your debts. A creditor must object within 60 days following the first date set for the Meeting of Creditors in the bankruptcy case.

But the time can be extended, so long as a motion to extend time is filed with the court before the 60 days runs. And subsequent extensions can be granted, so long as the subsequent motion(s) are filed before the deadline runs that was specified on the prior order. In re Gilbert, Bankr. SD TX 2013.