dedication - the quality of being dedicated or committed to a task or purpose - is an appropriate word to use in your given scenario, and can be used with the exact same wording you've provided:
Your dedication is admirable.
If the object of this dedication isn't implicit in the conversation, we can specify it in the sentence:
Your dedication to your children is admirable.
Your dedication to your work is remarkable.
I owe my life to the bravery and dedication of the rescue services.
If you wish to focus on their persistence, then perseverance - continued effort to do or achieve something despite difficulties, failure, or opposition - can also be used to describe that attribute.
His perseverance was rewarded: after many rejections, he finally found a job.
And both expressions can also be used in tandem:
Medicine is a field which requires dedication and perseverance.