ZOA Controller experienced operational error at FL370 during non radar oceanic procedures when failing to note an aircraft position report had inadvertently been deleted.

Narrative

During HNL rush; Aircraft X and Aircraft Y were transferred out. Aircraft X unaware to me had an amendment that changed the ELOYI time from XA04Z to XA43Z causing the data block to jump back into HNL's airspace. Aircraft X was at FL370. Aircraft Y had progressed to Oakland's airspace at XA11Z with a position report over ELOYI. At XA14Z Aircraft Y requested lower altitude down to FL350. With traffic at FL360; they were what appeared to be able FL370. I descended Aircraft Y to FL370 at XA47Z. Confusion occurred when Aircraft X started flashing overdue to ELOYI; but when Aircraft X was asked for position report; they reported over ERROT at XA50Z. Expecting a report over ELOYI; I questioned the flight and had them confirm position. The position had in fact been ERROT. Once I had updated the correct position; I climbed Aircraft Y up to FL380 and had regained separation at XA10Z. After looking through Aircraft X aircraft messages; it appears that a message containing Aircraft X's position report had been mistakenly deleted.