  It is well-known that the life span of solutions to Kirchhoff equations tends
to infinity when initial data tend to zero. These results are usually referred
to as almost global existence, at least in a neighborhood of the null solution.
  Here we extend this result by showing that the life span of solutions is
lower semicontinuous, and in particular it tends to infinity whenever initial
data tend to some limiting datum that originates a global solution.
  We also provide an estimate from below for the life span of solutions when
initial data are close to some of the classes of data for which global
existence is known, namely data with finitely many Fourier modes, analytic data
and quasi-analytic data.
