A "relentless" person is someone who keeps trying and never gives up.

"Relentless" is not a completely positive word; you can use it to describe someone who keeps doing something annoying as well. For example:

A: He sure does talk a lot, doesn't he?

B: Yes! Once you get him started, he is absolutely relentless!

You'll often hear the word "absolutely" before "relentless" to describe a person who's really, really determined.