The Collaborative International Dictionary of English v.0.48:

Overstay \O`ver*stay"\, v. t. [imp. & p. p. Overstayedor
   Overstaid; p. pr. & vb. n. Overstaying.]
   To stay beyond the time or the limits of; as, to overstay the
   appointed time; to overstay one's welcome. --Bp. Hall.
   [1913 Webster]