How long does it take before an academic article can no longer be kept behind a paywall?

Strictly speaking, the answer to your question is Never. Even after the copyright has expired, there is nothing to prevent a journal from keeping articles behind a paywall. Many journals will make articles open access after a certain amount of time, and after the copyright has expired, other people may freely distribute public domain articles. However, there are some journals that nonetheless have paywalled archives going back to the nineteenth century.

Some journals have in their copyright transfer some text regarding when the article becomes open access.

When that is not the case, I would expect that copyright laws apply, and the articles might become public domain after a certain period defined in law, see e.g.: https://en.wikipedia.org/wiki/List_of_countries%27_copyright_lengths

This is somewhat tangential to the question, but it's becoming increasingly common that governments, universities, and funding agencies require research to be published in an open access journal from the beginning.

Such policies are not retroactive – but paywalls are (very) slowly but surely becoming obsolete.