The Collaborative International Dictionary of English v.0.48:

Persevering \Per`se*ver"ing\, a.
   Characterized by perseverance; persistent. --
   Per`se*ver"ing*ly, adv.
   [1913 Webster]

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):

persevering
    adj 1: quietly and steadily persevering especially in detail or
           exactness; "a diligent (or patient) worker"; "with
           persevering (or patient) industry she revived the failing
           business" [syn: diligent, persevering]

Moby Thesaurus II by Grady Ward, 1.0:

124 Moby Thesaurus words for "persevering":
   Spartan, accepting, armed with patience, assiduous, balking, balky,
   bigoted, bound, bound and determined, bulldogged, bulletheaded,
   bullheaded, case-hardened, committed, constant, continuing,
   decided, decisive, dedicated, definite, determined, devoted,
   diligent, disciplined, dogged, dogmatic, earnest, endurant,
   enduring, faithful, fanatic, forbearing, hardheaded, headstrong,
   immutable, inalterable, indefatigable, indomitable, indulgent,
   industrious, insistent, intolerant, invincible, lasting, lenient,
   long-suffering, longanimous, loyal, mulish, never-tiring,
   obstinate, opinionated, overzealous, patient, patient as Job,
   permanent, perseverant, persistent, persisting, pertinacious,
   philosophical, pigheaded, plodding, plugging, preoccupied,
   purposeful, rapt, relentless, resolute, resolved, restive,
   sedulous, self-controlled, self-willed, serious, set, sincere,
   single-minded, sleepless, slogging, stable, steadfast, steady,
   stiff-necked, stoic, strong-willed, strongheaded, stubborn, sulky,
   sullen, tenacious, tireless, tolerant, tolerating, tolerative,
   unabating, unconquerable, uncooperative, undaunted, understanding,
   undiscouraged, undrooping, unfailing, unfaltering, unflagging,
   unflinching, unintermitting, uninterrupted, unnodding,
   unregenerate, unrelaxing, unrelenting, unremitting, unsleeping,
   unswerving, untiring, unwavering, unwearied, unwearying, unwinking,
   utterly attentive, weariless, wholehearted, willful