They are at a higher risk like your link provides but the studies within this link also show that most do not attempt another one. The majority (95%) according to the link you provided do not die by suicide after attempting and failing. Yes they are at higher risk but again my statement is correct.
This link does include people who died including in their first attempt at 58% but that is a different argument not people who have failed.
This study also showed this:
Which helps prove my point that if guns were not involved the chance of committing successful suicide are much much lower.The study also showed that the odds of successfully committing suicide are 140 times greater when a gun is used than for any other method.
Here is another quote from the article you quoted. Did you actually read beyond the headline?
“Most people who attempt suicide change their mind,” they wrote, adding that “most often, firearms do not allow for a change of mind or medical attention to arrive in time.