英文問題But the people who fail are 37 times more likely to succeed the second time?

The previous sentence:
Research shows that 19 out of 20 people who attempt suicide will fail.

The expressions "the first, second, third, fourth etc., next, last time" are often used as subordinating conjunctions to lead an adverb clause, telling which time of a number of times something has happened.

(something = people attempt suicide)
For example:
The first time people attempt suicide, they will fail 19 out of 20 cases, as reverted by a research.
The second time they do, they are 37 times more likely to succeed (than the first time).

To be strictly grammatical, we must add a preposition (e.g. at, for, ...) in front of those expressions to form an adverbial phrase if we want to modify the main verb (as an adjunct) in a single sentence.

Examples:
19 out of 20 people will fail at the first time (of attempting suicide).
People are more likely to succeed at the second time (of attempting suicide).

The key:
the second time ~ a noun phrase can be used as adverbial conjunction (so, can't be placed in the middle of sentence)
at/for the second time ~ adverbial phrase of time (adjunct)
a second time ~ adverbial phrase (meaning "again", "once again")

But the people who fail are 37 times more likely to succeed the second time (they attempt).
*** I think the speaker tried not to repeat what he had mentioned in the previous sentence by omitting the event (people attempt suicide).

But the people-------S
(who've failed to commit a suicide crime)------rel..cl
(and continued "to try again a 2nd time" to be-->on this issue)-------adv.phr.;.putting in the middle;
are 37 times more likely to suceed(=in the course of action)--------V.O.+phr.
------------------------------------------------------------------------------------
But the people (tried for the 2nd time) will finally suceed 37X more in committing suicide.
自殺無死間 , 才可放中間.

But the people who fail are 37 times more likely to succeed the second time?
句意講白一點 – 第一次的成功率低於2.8%,第二次的成功率是第一次的37倍。
副詞片語 – the second time – 第二次 – 原則上就需放在他所需修飭動詞(to succeed)前後，如修飭全句有時會置句首。但這句放在句尾已是很順，意為第二次會成功，如放在中間(?)!
因為不知你所說的中間在那，只好用猜的
Who fail (the first time – 隱意) the second time – 通嗎?
to the second time succeed – 不定詞被打亂了 - 通嗎?
more likely (副詞 ) the second time (? 詞 - 不知!) to succeed - 通嗎?