The Collaborative International Dictionary of English v.0.48:

Doggedly \Dog"ged*ly\, adv.
   In a dogged manner; sullenly; with obstinate resolution.
   [1913 Webster]

WordNet (r) 3.0 (2006):

doggedly
    adv 1: with obstinate determination; "he pursued her doggedly"
           [syn: doggedly, tenaciously]

Moby Thesaurus II by Grady Ward, 1.0:

43 Moby Thesaurus words for "doggedly":
   assiduously, bullheadedly, devotedly, diligently, faithfully,
   headstrongly, indefatigably, industriously, insistently, loyally,
   obstinately, patiently, perseveringly, persistently, persistingly,
   pertinaciously, ploddingly, relentlessly, resolutely, sedulously,
   sloggingly, stubbornly, tenaciously, tirelessly, unabatingly,
   uncooperatively, unfalteringly, unflaggingly, unflinchingly,
   unintermittingly, uninterruptedly, unregenerately, unrelentingly,
   unremittingly, unrestingly, unsleepingly, unswervingly, untiringly,
   unwaveringly, unwearyingly, wearilessly, willfully, with set jaw