Pores can form and grow in biomembranes because of factors such as the
rmal fluctuation, transmembrane electrical potential, and cellular env
ironment. We propose a new statistical physics model of the pore growt
h treated as a non-Markovian stochastic process, with a free energy ba
rrier and memory friction from the membrane matrix treated as a quasi-
two-dimensional viscoelastic and dielectric fluid continuum. On the ba
sis of the modern theory of activated barrier crossing, an analytical
expression for membrane lifetime and the phase diagram for membrane st
ability are obtained. The memory effect due to membrane viscoelasticit
y and the elasticity due to cytoskeletal network are found to induce s
harp transitions to membrane stability against pore growth and compete
with other factors to manifest rich dynamic transitions over the memb
rane lifetime.