The Collaborative International Dictionary of English v.0.48:

Inappetence \In*ap"pe*tence\, Inappetency \In*ap"pe*ten*cy\, n.
   [Pref. in- not + appetence: cf. F. inapp['e]tence.]
   Lack of appetency; lack of desire.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

56 Moby Thesaurus words for "inappetence":
   acedia, aloofness, anorexia, anorexia nervosa, apathy, ataraxia,
   ataraxy, benumbedness, blah, blahs, comatoseness, desirelessness,
   detachment, disinterest, dispassion, dullness, heartlessness,
   hebetude, hopelessness, indifference, insouciance,
   lack of appetite, languidness, lethargicalness, lethargy,
   listlessness, lovelessness, nirvana, nonchalance, numbness,
   passionlessness, passiveness, passivity, phlegm, phlegmaticalness,
   phlegmaticness, plucklessness, resignation, resignedness, sloth,
   sluggishness, sopor, soporifousness, spiritlessness, spunklessness,
   stupefaction, stupor, supineness, torpidity, torpidness, torpor,
   unambitiousness, unconcern, undesirousness, uneagerness,
   withdrawnness