The phrase "made a second attempt" is correct and usable in written English.
You can use it to describe an act of trying something again, usually after the first attempt failed. For example: "After failing to complete the task the first time, he made a second attempt and was successful."
The Yemeni government made a second attempt to offer support.
Mr. Issa made a second attempt to persuade her to change her mind.
He made a second attempt using pieces of an 18th-century Chippendale period clothes press.
It was almost an afterthought when, early last January, the town board made a second attempt to abolish the commission.
But today, barely a week after the company tried to have a major element in that finding reversed, it made a second attempt to fight it.
He made a second attempt with the Vísnabók (verse book, 1612), an anthology including Catholic poems such as Lilja purged of elements incompatible with Lutheran orthodoxy and new Reformation verses.
Even before the first race in Japan, in 1976, the Honda Motor Company had made a first attempt to create a Formula One team, from 1964 to 1968.
Last year, the commission made a first attempt at creating a blacklist when it published the names of 30 "non-cooperative tax jurisdictions".
He made a third attempt to deflect the Khans' criticism on Sunday, writing on Twitter that the real issue at stake in the election was terrorism.
It might not mean much in January, but last May, the likely Free Democrat foreign minister, Guido Westerwelle, made a first attempt at stating his international convictions.
The BNP leader Nick Griffin appears to have made a first attempt at launching himself into a career as a TV chef, with what threatens to be the first of many cookery programmes on BNP TV.
