Ailing

impregnable \im-PREG-nuh-buhl\, adjective:

1. Not capable of being stormed or taken by assault; unconquerable; as, an impregnable fortress.
2. Difficult or impossible to overcome or refute successfully; beyond question or criticism; as, an impregnable argument.

During this destruction the villagers . . . relied on their ancient instinct for survival and retreated to the impregnable fortress of the mountain.
-- Suheil Bushrui and Joe Jenkins, Kahlil Gibran: Man and Poet

What Spinoza says of laws is equally true of party-platforms,--that those are strong which appeal to reason, but those are impregnable which compell the assent both of reason and the common affections of mankind.
-- James Russell Lowell, "The Election in November", The Atlantic, October 1860

Impregnable is from Old French, from the prefix im-, "not" (from Latin in-) + prenable, "able to be taken or captured," from prendre, "to take," from Latin prehendere.