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Definition of ticklish : 1. Difficult; nice; critical; as, a ticklish business.
2. Sensible to slight touches; easily tickled; as, the sole of the foot is very ticklish; the hardened palm of the hand is not ticklish.
3. Standing so as to be liable to totter and fall at the slightest touch; unfixed; easily affected; unstable.

Synonyms:

precarious, irritable, thin-skinned, unstable, hypersensitive, continue, huffy, changeable, inconsistent, mercurial, freakish, unsteady, capricious, touch-and-go, change, erratic, frail, fragile, prickly, uncertain, unpredictable, awkward, inconstant, sensitive, fantastic, delicate, variable, volatile, whimsical, touchy, fantastical, easy, temperamental, fickle, finespun, soft, intricate, feisty

formidable, stressful, cumbersome, contrary, severe, arduous, knotty, demanding, harsh, oppressive, uphill, thorny, tricky, finicky, hard, fussy, troublesome, difficult, wearing, tough, strenuous, wearying, complicated, complex, cantankerous, tight, rugged, burdensome, wearisome, grinding, adverse, toilsome, laborious, rough, onerous, trying, bothersome

Usage examples:

• Owners have become ticklish of late, and do not care for strangers bringing an odd horse or two into their camp; however, I can make it all right with them, and Mr. Tuxford may send Lucky Boy here as soon as he likes. - "The Second String", Nat Gould.
• In certain directions and degrees of wind this was rather a ticklish task; but he had taken the precaution of putting up here and there a bit of rope. - "Donal Grant", George MacDonald.
• It is indeed a very ticklish theme to discuss. - "Moral", Ludwig Thoma.