plow on

7月7日のThe Japan Times Onlineの記事から引用します。 
U.K. PM Boris Johnson vows to plow on despite slew of resignations

結局PM Boris Johnsonも辞任を表明しましたが、その前に閣僚が辞任した時の記事でした。
"plow on" を辞書で見ます。
・Oxford English Dictionary: Continue steadily despite difficulties or warnings to stop.: ‘he plowed on, trying to outline his plans’
・Wiktionary: To continue with a menial, tedious or time-consuming task.: If you want to get good grades in the exam, you have to plow on with the book.
・Merriam-Webster: to continue doing something that is slow and difficult: I was discouraged, but I plowed on.