inexpugnable

adj.

1. Impossible to overcome or overthrow by force.
2. Impossible to put aside or drive away: inexpugnable dislike.

[Middle English, from Old French, from Latin inexpugnābilis : in-, not; see in-¹ + expugnābilis, capable of being overcome (from expugnāre : ex-, completely; see ex- + pugnāre, to fight; see impugn).]

inexpugnability in'ex·pug·na·bil'i·ty n.
inexpugnably in'ex·pug'na·bly adv.

[fr. L. in- + expugnabilis, capable of being overthrown]  /in-ik-SPUG-nuh-bul/  
impregnable, unassailable, invincible

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The adjective has one meaning:

Meaning #1: impossible to take by storm
  Synonym: impregnable

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