The TeXbook, page 454, last but one double dangerous bend paragraph
If a trial word l1 … ln has been found by this process, hyphenation will still be abandoned unless n ≥ λ + ρ, where
λ = max(1,|
\lefthyphenmin|) and ρ = max(1,|
\righthyphenmin|). (Plain TeX takes λ = 2 and ρ = 3.) Furthermore, the items immediately following the trial word must consist of zero or more characters, ligatures, and implicit kerns, followed immediately by either glue or an explicit kern or a penalty item or a whatsit or an item of vertical mode material from
\vadjust. Thus, a box or rule or math formula or discretionary following too closely upon the trial word will inhibit hyphenation. (Since TeX inserts
empty discretionaries after explicit hyphens, these rules imply that
already-hyphenated compound words will not be further hyphenated by
An explicit hyphen is a character whose character code matches the font's
\hyphenchar value or a ligature that ends with such a character (that's why also
--- inhibit hyphenation).
Indeed, if you try the following example, you'll see that TeX hyphenates the compound word:
The result is
The T1 encoded fonts have in position
0x7F a character which is identical to the normal hyphen. Changing the
\hyphenchar to denote this slot, the normal hyphen does not inhibit hyphenation any more.