per·se·vere 
(pûr′sə-vîr)
(pûr′sə-vîr)intr.v. per·se·vered, per·se·ver·ing, per·se·veres
To persist in or remain constant to a purpose, idea, or task in the face of obstacles or discouragement.
[Middle English perseveren, from Old French perseverer, from Latin persevērāre, from persevērus, very serious : per-, per- + sevērus, severe; see segh- in the Appendix of Indo-European roots.]
per′se·vering·ly adv.