[Quran 3:17] They are steadfast, truthful, submitting, charitable, and meditators at dawn.
[Quran 31:17] "O my son, you shall observe the Contact Prayers (Salat). You shall advocate righteousness and forbid evil, and remain steadfast in the face of adversity. These are the most honorable traits.
The Quran has many verses encouraging the Submitters (Muslims in Arabic) to be steadfast. In 31:17, steadfastness is mentioned as among the most honorable traits. In 3:146-147 we are told that God loves the steadfast. They pray for God's forgiveness and ask Him to strengthen their foothold.
[3:146-147] Many a prophet had godly people fight along with him, without ever wavering under pressure in the cause of GOD, nor did they hesitate or become discouraged. GOD loves the steadfast.
Their only utterance was, "Our Lord, forgive us our sins, and our transgressions, strengthen our foothold, and grant us victory over the disbelievers."
When faced with a test of adversity, Submitters seek help through steadfastness and the Contact Prayers (2:45, 2:153). Similarly, when dealing with seemingly insurmountable odds, the Quran gives us the example of Saul and the believers with him: they were aware that God's support allowed many a small army to defeat a large army (2:249-250). At the time of Muhammad, God tells us that twenty steadfast believers could defeat two hundred (8:65). When many new people joined Muhammad, and they were not as strong as they used to be, God decreed that a hundred steadfast believers could defeat two-hundred (8:66).
[2:153] O you who believe, seek help through steadfastness and the Contact Prayers (Salat). GOD is with those who steadfastly persevere.
David and Goliath
[2:249] When Saul took command of the troops, he said, "GOD is putting you to the test by means of a stream. Anyone who drinks from it does not belong with me―only those who do not taste it belong with me―unless it is just a single sip." They drank from it, except a few of them. When he crossed it with those who believed, they said, "Now we lack the strength to face Goliath and his troops." Those who were conscious of meeting GOD said, "Many a small army defeated a large army by GOD's leave. GOD is with those who steadfastly persevere."
[2:250] When they faced Goliath and his troops, they prayed, "Our Lord, grant us steadfastness, strengthen our foothold, and support us against the disbelieving people."
Steadfastness is frequently mentioned as a trait of the righteous (3:17, 29:58-59, 31:17, 33:35, 38:44, 50:32, etc.).
[50:31-33] Paradise will be offered to the righteous, readily. This is what was promised to every repenter, steadfast. They reverenced the Most Gracious, in their privacy, and came wholeheartedly.
In addition to steadfastly persevering during adversity (2:177, 6:34, 14:12, 22:35), God encourages the believers to steadfastly persevere in worshiping Him and carrying out His commands (19:65, 52:48, 68:48). We are told that if we repent, believe, lead a righteous life and steadfastly remain guided, then God will surely forgive us (20:82).
[19:65] The Lord of the heavens and the earth, and everything between them; you shall worship Him and steadfastly persevere in worshiping Him. Do you know of anyone who equals Him?
[52:48] You shall steadfastly persevere in carrying out your Lord's command―you are in our eyes―and glorify and praise your Lord when you get up.
[20:82] I am surely Forgiving for those who repent, believe, lead a righteous life, and steadfastly remain guided.
We are also encouraged to remind one another to be steadfast.
[90:11-17] He should choose the difficult path. Which one is the difficult path?
The freeing of slaves. Feeding, during the time of hardship.
Orphans who are related. Or the poor who is in need.
And being one of those who believe, and exhorting one another to be steadfast, and exhorting one another to be kind.
[103:1-3] By the afternoon.
The human being is utterly lost.
Except those who believe and lead a righteous life, and exhort one another to uphold the truth, and exhort one another to be steadfast.
May God grant us steadfastness and let us die as submitters (7:126).