Answer: "The successful maintenance of a prolonged oceanic war" refers to the ability of a nation or military to sustain and effectively prosecute a war that is primarily fought on or over the oceans, for an extended period of time.
In this context, "successful maintenance" means that the country or military is able to provide the necessary resources, equipment, and manpower to continue the war effort over a long period, while achieving its military objectives and minimizing the negative impact on its own population and economy.
"Prolonged oceanic war" specifically refers to a conflict that takes place primarily on the oceans, such as naval battles or submarine warfare, and which is likely to last for an extended period of time, such as several years. Examples of such wars include World War II's Battle of the Atlantic, the Anglo-Dutch Wars of the 17th century, and the Napoleonic Wars' Continental System.
Explanation: In this context, "the successful maintenance of a prolonged oceanic war" refers to the ability of the British to sustain and effectively prosecute a war that is primarily fought on or over the oceans for a long time, even if they were to lose control of Egypt and the Middle East to the Axis powers (Germany, Italy, and Japan).
Churchill disagreed with the idea that losing control of Egypt and the Middle East would be a "mere preliminary" to the successful maintenance of a prolonged oceanic war. He acknowledged the grave (or mortal) consequences of such a loss, given the daunting proposition of fighting a war against an Axis system controlling most of Europe, Africa, and Asia. He expressed concern that, without more advanced positions by the United States, the war could tilt heavily in their disadvantage.
Overall, the phrase "the successful maintenance of a prolonged oceanic war" refers to the ability to sustain a war effort over a long period, while achieving military objectives, even in the face of significant challenges and setbacks.