Can gen_id be shared between chats.?

I created a image and using the gen_id I have created more variations of that image.
The variations is exactly matches the gen_id. All good.

I have created close to 50 images and Dall-e says I have reached the limit.

Came two days later to continue on the same chat window. I got the same message.

I opened a new chat window and used the same gen_id to create, but i got different result. I cannot able to replicate the same variation like used in the first chat window. I went back to the previous chat window and copied the exact prompt and tried, the result was different.

My question is
Can gen_id be shared between chats. If yes, how?