We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability S(t) in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. S(t) is shown to exhibit a simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical scanning tunneling microscopy data on step fluctuations on Al/Si(111) and Ag(111) surfaces.