The filament is rapidly becoming hotter, and thus rapidly undergoing thermal expansion. During this expansion, any small imperfection may cause it to break.
Once the bulb is in steady-state, the filament no longer grows hotter, and no longer expands.
The effect is much worse if your bulb is being dimmed by a cheap dimmer switch, because even though the filament is getting less power, it's getting it in a very choppy form that often causes the filament to oscillate and buzz. Better dimmers have a choke and some capacitors to help smooth out the choppy signal coming from the triac.