Always is a very long time. What we call the lifetime exclusion was introduced in 2014. Since then public offers have included this sentence or similar:

Welcome offer not available to applicants who have or have had this Card

In practice the lookback period is not lifetime, but about 7 years since the same card was closed. Some targeted offers include this sentence, some do not. If it is not in the terms, it does not apply, but there are other reasons that a bonus can be denied:

https://www.flyertalk.com/forum/amer...ne-2018-a.html