When we shower upstairs there is a sewer gas smell coming from from the downstairs toilet. I have replaced the wax gasket twice. What is the problem?

Here's what I think is happering. You shower upstairs and the discharge picks up speed dropping down from the second floor. You have a partial blockage downstream from the downstairs toilet. The discharge from the shower hits that and bounces back sending a bubble of sewer gas ahead of it before it drains away. The solution would be to pull the toilet and snake from there. Good luck, Tom