indefatigable (adjective) – tireless, not giving up

indefatigably (adverb) – tirelessly, not giving up

indefatigability or indefatigableness (noun) – be untiring

Here are some examples of how you can use it:

Our indefatigable reporter was turned away at the border numerous times, but she kept trying to get inside.

His indefatigable spirit refused to see the hopelessness of the situation.

Thank you for working indefatigably on the project, even working at weekends if needed.

I admired the children’s indefatigability in trying to make our new neighbours feel at home in their new surroundings.