The Collaborative International Dictionary of English v.0.48:

Persevere \Per`se*vere"\, v. i. [imp. & p. p. Persevered; p.
   pr. & vb. n. Persevering.] [F. pers['e]v['e]rer, L.
   perseverare, fr. perseverus very strict; per + severus
   strict, severe. See Per-, and Severe.]
   To persist in any business or enterprise undertaken; to
   pursue steadily any project or course begun; to maintain a
   purpose in spite of counter influences, opposition, or
   discouragement; not to give or abandon what is undertaken.
   [1913 Webster]

         Thrice happy, if they know
         Their happiness, and persevere upright.  --Milton.
   [1913 Webster]

   Syn: To Persevere, Continue, Persist.

   Usage: The idea of not laying aside is common to these words.
          Continue is the generic term, denoting simply to do as
          one has done hitherto. To persevere is to continue in
          a given course in spite of discouragements, etc., from
          a desire to obtain our end. To persist is to continue
          from a determination of will not to give up. Persist
          is frequently used in a bad sense, implying obstinacy
          in pursuing an unworthy aim.
          [1913 Webster]

WordNet (r) 3.0 (2006):

persevere
    v 1: be persistent, refuse to stop; "he persisted to call me
         every night"; "The child persisted and kept asking
         questions" [syn: persevere, persist, hang in, hang
         on, hold on]

Moby Thesaurus II by Grady Ward, 1.0:

77 Moby Thesaurus words for "persevere":
   abide, abide with, balk, bear, bear with, beat the game,
   beat the system, bide, brave, brook, carry on, carry through,
   cling to, come through, come up fighting, come up smiling,
   continue, decide, die hard, endure, get along, get on, go on,
   go on with, hang in, hang in there, hang on, hang tough, hold out,
   keep at, keep at it, keep driving, keep going, keep on,
   keep trying, keep up, last, live through, lump, lump it, make out,
   manage, never, never say die, not accept compromise, not budge,
   persist, press on, proceed, put up with, resolve, see it through,
   see through, stand, stand fast, stand firm, stand for, stand out,
   stand pat, stick, stick it out, stick to, stick to it, stickle,
   stop at nothing, suffer, support, survive, sustain, take no denial,
   take up with, tolerate, triumph, weather out, weather the storm,
   win out, win through