Samuel Johnson, A Dictionary of the English Language (1756) has this not-at-all-ominous entry for predicament:
PREDICAMENT. s. {predicament, Fr. prædicamentum, Lat.} 1. A class or arrangement of beings or substances ranked according to their natures: called also categorema or category. Digby. 2. Class or kind described by any definitive marks. Shakespeare.
Noah Webster, A Compendious Dictionary of the English Language (1806) likewise offers no hint that predicament may lean toward the negative:
Predicament, n. a class, arrangement, kind, state
The same is true of Webster's first massive dictionary, An American Dictionary of the English Language (1828):
PREDICAMENT, n. {Fr. from L. prædicamentum, from prædico, to affirm.} 1. In logic, a category ; a series or order of all the predicates or attributes contained under any genus. The school philosophers distribute all the objects of our thoughts and ideas into genera or classes, which the Greeks call categories, and the Latins predicaments. Aristotle made ten categories, viz. substance, quantity, quality, relation, action, passion, time, place, situation and habit. {Encyc.} 2. Class or kind described by any definite marks ; hence, condition ; particular situation or state. {Shak.} We say, the country is in a singular predicament.
The example Webster chooses here is interesting in that it could as well be used to convey the sense that the country is in a parlous state as to present it as being in a situation of unspecified positives or negatives. The landscape changes with Webster's revised American Dictionary of the English Language (1847), which repeats the two definitions from the 1828 edition but then adds a third before the final remark that "We say the country is in a singular predicament":
3. Sometimes, a bad condition or position. {Colloquial} Smart. We say the country is in a singular predicament.
The subsequent American Dictionary of the English Language (1864) draws the negative sense of the term farther into the basic meaning of the word:
Predicament, n. [Derivation omitted.] Class or kind described by any definite marks; hence, condition; particular situation or state; especially, an unfortunate or trying position or condition. "O woful sympathy, piteous predicament." Shak. ... Syn.—Category; condition; state; plight.
The continuing evolution of the term is recorded in Webster's New International Dictionary (1909):
predicament n. [Derivation omitted.] 1. That which is predicated or asserted ; a class or kind described by any definite marks. Specif.: Logic. = CATEGORY, 1. 2. Condition, ; situation ; state ; esp., an unpleasant, unfortunate, or trying position, condition, or situation. "O woful sympathy, piteous predicament." *Shak.*3. Preaching. Obs. and R.
Syn.—PREDICAMENT, PLIGHT, QUANDARY, DILEMMA are here compared in their nontechnical senses. PREDICAMENT and PLIGHT were originally applicable to good as well as bad conditions, but now commonly connote as their modifier "bad," "evil," or the like ; predicament applies esp. to situations or positions, plight, to states or conditions, which are unfortunate, trying, or unpleasant ; as, "Advice ... may be of such nature that it will be painful to reject and yet impossible to follow it; and in this predicament I conceive myself to be placed" (Crabbe) ; "Had I but seen thy picture in this plight, it would have madded me : What shall I do now I behold thy lively body so?" (Shak.).
And finally, Ernest Weekley, An Etymological Dictionary of Modern English (1921) has this entry for predicament:
predicament. F. prédicament, Late L. praedicamentum (see predicate), used to render Aristotle's κατηγορια, category of predications. Mod. sense is narrowed from gen. sense of class, condition.
Irish ladies of strict virtue, and many northern lasses of the same predicament (Tom Jones).
Conclusion
It thus appears that predicament underwent a transformation from meaning "[uncharacterized] situation" to meaning "bad situation" in the course of about a century (1806–1909)—and that it did so through the natural process of evolving popular usage, centuries after it first emerged as an English word.