During this time has your hens molted? If they are the same age that could be it. I can not see all of them stopping at the same time. Do you have a sneaky snake, large rat or other preditor who could sneak in and get the eggs. A two legged one either. Some RIR are actually production reds who will stop after 2 or three years but not at the same time. Do you hear the egg song that the hen does when she lays eggs. Something here is off. Please check more closely.
For a long time layer you need birds that are not production types. You may get one or two less per week but they lay a long long time. Others have quoted some laying an egg occ for 6 or 7 years. When I rear a hen I want her in production a long time. After all we wait anywhere from 18 weeks to 28 weeks for eggs to start. That is an investment of time and feed. I also get attached to my hens and do not want to cull them. They get names for crying out loud after they make known that they are hens. I like the orphingtons, NH, Delaware hens. The EE's are also good layers for me.
Now if you are a big production egg facility you would plan new pullets to take up the slack and put all out at once to cull. Starting with new pullets laying as the old ones quit. Then you would want the production red, comet , cinnamon queens etc. I hope you get an answer that will help you. Gloria Jean