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It's been a day and no has posted a truly elegant, natural, and general solution, so I'll post a narrow one. By default, a message is stopped when it occurs three times in $MessageList. One can reduce the number of times a message is printed by pre-loading $MessageList with it. Block[{$MessageList}, Unprotect[$MessageList]; $MessageList = ...


Here is a method using Off and On triggered by the first appearance of the message. I avoid unprotecting any System Symbols by using TagSetDelayed. I use $Post to turn the message back on. Modification of your function is not required; this operates via the low-level Message system. Code: badness::oops = "Watch out! Result could be ...

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