数年間ぶっ続けでを英語でなんと言うか？

Nth year running, N years runningともいえます。もちろん、数日、数ヶ月と応用が利きます。 0:06 and for the 6th year running, Singapore has ranked number one as the top place to do business in the world.

BBC News Singapore vs Hong Kong who wins
https://www.youtube.com/watch?v=ZgHZjeubX68  0:13 Camry, the name roughly translates to the Japanese word for Crown, and it is the king of sales being the best selling passenger car in the US for the past 12 years running. 日本のクラウンの相当するカムリはアメリカで12年連続で販売第一位の実績を持つセダンだ。
2015 Toyota Camry | Driven: Car Review | The New York Times
https://www.youtube.com/watch?v=O2w39SEZQpU  2:26 Zane made huge contributions to his sport during his era, aside from winning the Mr. Olympia crown three years running from ‘77-’79, this muscleman inspired a shift that saw the focus move away from pure mass and towards a competitor’s proportions and aesthetics. ボディービルダーのフランクゼインさんは三年間続けてミスターオリンピアに輝いたばかりでなく、ボディビルは身体を筋肉隆々にするだけのスポーツではなくプロポーションと筋肉の分け目の美学という分野に発展させた。
Top 10 Famous Male Bodybuilders

参考リンク
http://bridge-english.blogspot.jp/2014/09/in-row.html  in a row