Firstly. You should never remove the male before the birth of the first litter, the father plays an important role in bringing up the pups. You are advised to remove the male before the arrival of the second litter.
Females will not kill and eat their pups unless there are problems. These problems can be genetic. It is best to not continue breeding with any female that kills her pups for no apparent reason.
How long are you giving each female to recover from each pregnancy?
Also, it is a common myth that you shouldn't go anywhere near the pups shortly after birth. Female gerbils are very tolerant of their pups being handled, not that i would recommend any novice gerbil breeder to do so.
I often handle gerbil pups within a few hours after birth so that i can check that they have full tummies.
Are you giving the pregnant and lactating females any additional proteins?