I'm sorry for your loss.
Did you happen to take any photos?
You looked in the vent and saw several partially formed eggs - were these in the abdominal cavity or the oviduct?
Did it look like either of these...
Hi Welcome To BYC
What type of food/treats do you feed?
How old are they?
Any photos?
You are seeing a fully formed egg in the oviduct - is it partially sticking out when the hen dies?
Since you are losing several birds a week - as @MasterOfClucker suggests, having a necropsy would be...