RI Expires....?
The situation you describe should be covered in the Pre amble to the MEL.
Additionally the OPs Manual will give you the answer - or should do!
From my experience in compiling both MELS and CAMES for a number of operators, the effective day of an MEL item commences at mid night on the day it was discovered and terminates at midnight on the last day of permitted operation. If your organisation has an approved RIE procedure then an extension of the original RI would/could be granted by the agreed signatory to the RIE, normally a senior Pilot, i.e.Fleet captain.
MB