Here ‘dogged’ (two syllables with the stress on the first) means ‘persistent’.
The proverb teaches perseverance and the determination to succeed. Stick to it
and you will achieve your object.

##### See also:

* Constant dripping wears away the stone
* If at first you don’t succeed, try, try, try again
* Little by little and bit by bit
* Little strokes fell great oaks
* Rome was not built in a day
* Slow but sure wins the race
* Where there’s a will there’s a way