The phrase "able to persevere and" is correct and usable in written English.
You can use it when discussing someone's ability to endure challenges or difficulties, often in a motivational or inspirational context.
Example: "Despite the obstacles she faced, she proved to be able to persevere and achieve her goals."
Alternatives: "capable of enduring and" or "able to persist and".
"Through adversity, through everything we've been through, we've been able to persevere and win back-to-back championships.
"Through adversity, everything we have been through, we have been able to persevere and to win back-to-back championships.
Through adversity, through everything we've been through, we've been able to persevere and to win back‑to‑back championships.
"Which is to be able to persevere and succeed, to overcome this obstacle and to deal, to withstand, whatever we have to endure".
"Today's players can learn about humility, about self-respect, about being able to persevere and keeping your eyes on the prize.
How China can successfully stage the Beijing Olympics in less than three months in an open question, but there have been past instances where countries that have suffered devastating disasters were able to persevere and put on huge world sporting events.
If we want kids to be able to persevere through difficulties and deal well with criticism and complications and be able to concentrate on things for a long period of time--all of these things that are really hard to measure on tests of kindergarten readiness but turn out to be really important in terms of kids overall success, it's those first three years that are so important.
To be able to persevere, reinvent myself and give the kids the benefit of all my experiences — I couldn't have predicted that, but I'm glad it happened".
If West leads his singleton heart, East will be able to persevere with that suit and give his partner two overruffs.
Their technical ability and tactical savvy set them apart, and they were able to persevere despite the devastation the country has experienced recently.
But I still love animals, and admire the people able to persevere through veterinary school, in the face of daunting odds and heavy financial challenges, to care for them.
