This site is not the only one that this is happening to. Another site I regularly visit has a solution:
We're having significant issues with spam, which is time-consuming for moderators to find and delete.
Here's how most of it works: Someone new joins the forum. Their first post(s) bumps an old thread with an unobjectionable but only vaguely relevant comment. For instance, if the old thread was about keyword choices for Amazon ads, the new post might be something like, "Thanks for the great information! Advertising is so important." At some point -- days or weeks later -- the spammer returns to their vague post and inserts a spam link. By this point, the thread has fallen off the front page, so moderators don't notice the edit.
To keep the forum as spam-free as possible, Ann and I have been tracking vague bumps of old threads, returning to check them, day after day, to catch the point at which they are edited to include spam links. When we see that happen, we ban the spammer and delete the post. But this practice has become quite time-consuming for us. Furthermore, the bumped zombie threads are an annoyance to legitimate members, who waste time responding to some question that was asked in 2014 by someone who's no longer even here.
I don't want to disallow the bumping of old threads, because sometimes old issues do regain relevance. So I think our rule is going to be that you should not bump an old thread unless your post 1) is clearly and specifically relevant to the thread topic, and 2) makes it clear why you have chosen to bump the old thread instead of beginning a new one.
This rule means that any post that bumps an old thread in a way that seems vague or not specifically relevant will be deleted, even if it doesn't have a spam link visible.
Thoughts or objections? Any reason we should not do this? Input appreciated!