Why do protective relays have a delay?
You really need to provide more information as to what are the particulars of your system as there are many varieties of protection relays.  In any case, delays are often used to prevent nuisance tripping due to transient events because many devices protected by relays can tolerate short term faults while the consequence of tripping can be significant.  For example, suddenly taking a part of the power grid offline can cause damage to equipment.