You don’t indicate the incoming amperage of the main breaker. Do you have 60A, 100A or 200A service? I would suspect that you have 60A. If the main breaker is tripping I would change that and not the breaker for the dryer. The dryer takes a 30A double breaker (240V) right?
Here’s what happens over time… When a breaker runs at or near capacity (capacity here means approx 80% of load), over time, the internal mechanism can begin to change. When this happens one of two things happen, either the breaker gets real sensitive and trips before it should (like in your case I suspect) or the breaker will not trip even when the power through it exceeds its rating.
Based upon your reported symptoms, I would suspect that the main breaker is faulty. Have an electrician check and/or replace it.
Dan