The phrase "after persisting" is correct and usable in written English.
It can be used to indicate that something occurred following a period of persistence or effort.
Example: "After persisting through numerous challenges, she finally achieved her goal."
Alternatives: "after enduring" or "after continuing".
"My father was skeptical," he continued, but after persisting he got one.
Arsene Wenger was heavily criticised by Arsenal supporters after persisting with Mathieu Flamini against Southampton.
After all, it is reasonably suspicious that, after persisting for more than a hundred centuries, the ice began to vanish in the very century in which humans started to change the environment both globally and, perhaps more important, locally.
After persisting with poetry for a while, he had sudden success in 1959 with his first play, The Zoo Story, written in two and a half weeks before his 30th birthday.
First, Mr Cameron would struggle to justify removing Dr Fox after persisting with Vince Cable, the Liberal Democrat business secretary, who barely bothers to hide his distaste for the Conservatives.
A broad area of disturbed weather formed in association with the wave and the low-level circulation, and after persisting for several days developed a smaller low-level circulation on August 29 about 575 miles (925 km) south-southeast of Cabo San Lucas.
The streaking and trailing and after-imaging persisted for days.
It demonstrated strong stability with a relative current of 95% still persisting after 40 000 s.
Declines in circulating Ang II observed after aliskiren monotherapy persisted after dual blockade.
After he persisted, his master ordered his mother to beat him.
But discrimination and violence against the indigenous Mayans continued long after, and persist today.
