How is the faculty of persistence developed?

I think that to strengthen your persistence and banish laziness, so to speak, one should concentrate on strengthening the bond that you have with yourself.

Mindfulness alone can have a great impact on the way you see yourself internally and can increase your need or desire to satisfy yourself.

Though, overall I think persistence is something you gain over time, by being conscious of negativity and a lack of motivation, and knowing how to react to such emotions.

I have had a look around and everywhere I look seems to relay the same message:

Lack of persistence is often present due to the absence of faith (or self belief)

How is the faculty of persistence developed?

Persistence is cultivated by

• guarding and abandoning
• developing and maintaining

One way to guard and abandon unwholesomeness while developing and maintaining wholesomeness you have to note what has arisen within you.

• Aversion / unpleasant feeling - something is not agreeable
• Craving / pleasant feeling - something is agreeable
• Ignorance / neutral feeling - you are neutral to the experience yet not in touch with the the true nature of the experience

By maintaining total equanimity with the knowledge of arising and passing then you abandon and develop. Though this analysis what is abandoned is the roots or defilements and what is developed is the 7 Enlightenment Factors leading to Disillusionment and Revulsion (Nibbida).

For more detailed and comprehensive explanation see: Wings to Awakening - The Four Right Exertions by Thanissaro Bhikkhu

Also see: Right Effort - samma vayamo

how do you banish laziness?

Laziness or lethargy is abandoned through development of the sense of urgency. Contemplation of death is one of the main meditation tools for this. Live each breath as it is your last trying (see: (Aṭṭhaka) Maraṇa,sati Sutta 1) to establish mindfulness or conduct your activities without procrastination. This should be done at least twice a day when the day breaks and day ends contemplating that mishap may end your life and time will run out on what needs to be done. Also see: Maraṇa Sati Kathā and How to do “contemplation of death” meditation? and is it dangerous?

“But how, bhikshu, do you cultivate the mindfulness of death?”

“Here, bhante, I do it thus:

'Indeed, should I live just the time it takes to breathe in and then out, to breathe out and then in, I would wisely attend to the Blessed One’s teaching, much indeed would be done by me!'

Thus, bhante, I cultivate the mindfulness of death.”

Source: (Aṭṭhaka) Maraṇa,sati Sutta 1 and also similar passage is in: (Chakka) Maraṇa,sati Sutta 1

Sloth and Torpor can also contribute to laziness as this makes you drowsy and sleepy. This can be a big hindrance especially during meditation. One way to abandon it is similar to the method outlined above. Especially see the section on Insight towards the end of Pacala Sutta

“Nothing is worth clinging to”

When this was said, the venerable Mahā Moggallāna said this to the Blessed One: “In what way, bhante, in brief, is a monk freed through the destruction of craving, that is, one who has reached total perfection, the total security from bondage, the total holy life, the total consummation, the highest amongst gods and humans?”

“Here, Moggallāna, the monk has learned that nothing is worth clinging to. And, Moggallāna, a monk has learned that nothing is worth clinging to, thus: he directly knows all things [he directly knows the nature of the all]. Having directly known the nature of all things, he fully understands all things.

Having fully understood all things, he knows whatever feelings there are, whether pleasant, painful or neither painful nor pleasant.

As regards to those feelings,

he dwells contemplating impermanence in them;

he dwells contemplating dispassion [fading away of lust] in them;

he dwells contemplating ending (of suffering) in them;

he dwells contemplating letting go (of defilements).

When he dwells contemplating impermanence in them, contemplating dispassion in them, contemplating ending in them, contemplating letting go, he does not cling to anything in the world. Not clinging, he is not agitated; being not agitated, he himself surely attains nirvana.