The phrase "ineffective argument" is correct and usable in written English.
You can use it when you want to describe an argument which is not effective or persuasive. For example, "The lawyer's argument was ineffective and the judge was not persuaded by it."
Yet, myopic Republicans cling to the overused and ineffective 30 year argument.
When colleges and universities explain by talking about generous state, federal and institutional aid, it becomes an ineffective "second tier" argument that looks defensive and opens higher education to the perennial American consumer battle over the appropriate use of tax dollars.
It does seem as though the wars that sought to bring democracy to some of those countries were, at least as a form of liberalizing or modernizing argument, entirely ineffective and arguably counterproductive.
Worrall (2009) maintains that these contentions are ineffective against the miracle argument because they depend crucially on a misleading formalization of it in terms of probabilities.
If so, then the fine-tuning argument is ineffective: the probability of fine-tuning on the many worlds suggestion together with atheism is at least as large as the probability of fine-tuning on theism.
Prof. Howard W. Woodward of Western Reserve University has spent 6 years studying subject, that arguments are ineffective in changing people's minds, in 80% of cases.
This will then mean that such arguments are ineffective against very radical forms of skepticism, which doubt the laws of logic, and/or which refuse to accept any starting point as uncontentious; and it will also mean that they may be effective against a skeptic who is prepared to accept some starting point, but then ineffective against another skeptic who is not.
The judge then accepts the arguments that ineffective teachers are "disproportionately situated in schools serving low-income and minority students," that "there are a significant number of grossly ineffective teachers currently active in California classrooms," and that California's tenure statutes inappropriately shield ineffective teachers from dismissal.
Similarly, an argument that is ineffective because it is not understood can become relevant once the audience is better informed.
