A rough estimate of the endurance limit for steels is 50% of the tensile strength, plus or minus 10%. Normalized chrome moly has a tensile strength between 95 and 100 ksi, as I remember. This is stronger than a lot of mild steels and the endurance limit is also greater. This provides more fatigue resistance, as Tom says.
The problem with the problems I dealt with was as the builder, often a well respected manufacturer, used much thinner wall tubing in the chrome moly applications. This is typical. Stress is force divided by area, so the stresses from the cyclic loads in the thinner wall tubes were as close, or closer, to the endurance limit as with the typical thicker wall mild steel frame. The dang things broke. Also, they flexed a lot under use and the handling was spooky at best.
Builders, and especially me, figured out that the welds needed to be normalized to prevent cracking. This sorta worked. Sometimes we normalized the weld area, other instances we annealed it, or we did not get it hot enough to do any good. One thing we learned is the thinner wall chrome moly worked best for trellis like space frames. Bending loads are minimized and replaced by tensile and compression loads in these structures. Why this frame type works better, I have no clue. There is a book by Carroll Shelby, "Engineer to Win," that has some hints on using this metal.