Stage travel in the Old West was always fraught with mechanical and environmental problems.  That is not to say that every journey was delayed.  Just most of them.   Stages out of larger cities were often the "Concord" style with soft seats, better suspensions and were generously appointed making for a better image of the stage line with the traveling public.   But once away from really well maintained roads, the vehicles usually gave way to the humble and plain "Mud Wagon" which was rougher, poorly slung from the chassis, and mostly battered your bones inside your body for the rest of the trip. However, considering the rough Western roads, the Mud Wagons handled the punishment. 

Since there was no "1st Class," no one complained much.