Why do we say "If at first you don't succeed, try, try again"?

Meaning:

Keep trying, and you will succeed

Background:

Many sources say that the first known written record of this proverb is in American educator Thomas H Palmer's Teacher's Manual (1840):

'Tis a lesson you should heed,
Try, try again.
If at first you don't succeed,
Try, try again.

And that Edward Hickson later popularized it in his book The Singing Master. But if sources are correct, The Singing Master was published in 1836, placing it earlier than Palmer's work.

Either way, it seems there is agreement that it was Edward Hickson who popularized the adage through his moral song, the full lyrics of which are:

'Tis a lesson you should heed–
Try again;
If at first you don’t succeed,
Try again.
Then your courage should appear;
For if you will persevere,
You will conquer, never fear,
Try again.

Once or twice though you should fail,
If you would at last prevail,
Try again.
If we strive, 'tis no disgrace
Though we did not win the race–
What should you do in that case?
Try again.

If you find your task is hard.
Try again;
Time will bring you your reward,
Try again;
All that other folk can do,
Why with patience should not you?
Only keep this rule in view,
Try again.

Some say that the essence of the expression has its roots long before this date, pointing to Robert 1 of Scotland (Robert the Bruce), a 14th century king who, the legend says, having suffered a major defeat at the hands of the English, went into hiding in a cave near Gretna (close to the border of Scotland and England). While there he watched a spider trying to spin a web. Each time the spider failed, it simply started again. The story goes that Robert was so inspired by the little arachnid that he left the cave and returned to lead his troops in a series of victories against the English.

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