What will you call a person with an endless spirit of pursuing something?
- Firmness of purpose; resolve: approached the task with determination and energy.
- A fixed intention or resolution: returned to school with a determination to finish.
also unyielding or tenacious :
- Not bending; inflexible
- Not giving way to pressure or persuasion; obdurate.
The word Doggedness comes to my mind.
In some situations single-mindedly would also be useful.
Undeflectable, undeterrable and indefatigable use litotes.
Unswerving perhaps does too.
Compelled or compulsive relate to monomania, an unhealthy drivenness.
Adjectives describe a noun.
More positive connotation: impassioned, fervent, wholehearted, unwavering, steadfast, pledged, dedicated, driven
Less positive connotation: preoccupied, haunted, obsessed, plagued, consumed, tormented
Simile might help:
"He was not unlike Pacman in his constant quest for junk food."
What came to mind when reading the question was relentless.
- oppressively constant; incessant.
- that does not relent; unyieldingly severe, strict, or harsh; unrelenting:
"His relentless pursuit of perfection was his undoing."
"Grit" is a great word for this personal trait.
A person with grit has perseverance, zeal, resilience, and determination. Source: Grit (personality trait) on Wikipedia
If it was a case of continuing when the odds of success are diminishing, but you didn't want a word with connotations of mental illness or stubbornness, I'd go with persevering.
Volition perhaps fits according to some sources.
Ambitious, Dictionary.com, adjective, 1. having ambition; eagerly desirous of achieving or obtaining success, power, wealth, a specific goal, etc.
It's quite ambitious to pursue something with endless spirit.
How about perseverance: \ˌpər-sə-ˈvir-ən(t)s\
- The quality that allows someone to continue trying to do something even though it is difficult.
- Continued effort to do or achieve something despite difficulties, failure, or opposition.