Mating more than once?

Males of many, if not all, species will happily mate on several occasions; the quality of sperm may deteriorate on later occasions but not for the first couple of times. Some females may mate more than once but this is much rarer and I don't know if it's strictly necessary. In some butterflies such as Parnassius the females could not mate again because of the sphragis. In the small frits such as Euphydryas and Melitaea there is a waxy deposit left on the female's abdomen after mating so it is easy to tell if a female has mated or not; whether this prevents further mating I'm not sure.

Bob