When it was built in the 1960s the ICBMs that could hit wouldn't have destroyed it however more accurate, more powerful bunker buster nukes came about. Neutron bombs would also wipe it out. Today its the NORAD alternate command site and its being renovated as part of a 700 million dollar operation to make NORAD operations not be affected by EMP affects from nukes or other means. Its more hardened against nukes then most gov't command centers that are known to the public or military intel.
In Independence Day the aliens had destroyed the Cheyenne Mountain base and other nearby military bases. In Independence Day Resurgence it had been rebuilt and fortified hence why the aliens sent a breaching party to assault rather then just try to blast it apart like last time. When you fortify against one type of attack you unfortunately can weaken the base against some other types of attack.