The initial condition in your flipflop is never met if the tag is split between lines. You've read the '<B' but not the 'ird'.

Try setting local $/ = '=+=+=+=+=+=+=+=+=+=+=+'; and admitting optional whitespace between tag characters.

{
    local ($/,$_) = ('=+=+=+=+=+=+=+=+=+=+=+');
    while (<>) {
        s/<\s*?B\s*?l\s*?u\s*?e\s*?b\s*?i\s*?r\s*?d\s*?>.*$//s;
        print
    }
}
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By dealing with the whole chunk, you don't need the flipflop operator.