The Collaborative International Dictionary of English v.0.48:

Limpsy \Limp"sy\ (l[i^]mp"s[y^]), Limsy \Lim"sy\ (l[i^]m"s[y^]),
   a. [See Limp, a., and cf. W. llymsi having a fickle motion,
   weak. Cf. Flimsy.]
   Limp; flexible; flimsy. [Local, U. S.]
   [1913 Webster]