Definition of "press on" []

• To persist, continue to advance (verb)

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• "But whether because of his determination to catch the rebel king Bessus or because he thought that a prolonged period of inactivity so soon after the Philotas affair might serve to fan the fires of discontent, Alexander decided to press on through the winter snows toward the peaks of the Hindu Kush."
• "Helped via communicator by a young teen named Brandon Justin Long, the two press on until they find themselves teetering warily on a bare metal beam high over a dangerous chasm."
• "If the unmanned test launch of the N-1 worked, the Soviets were prepared to press on with their clandestine manned lunar program, a program that Kremlin leadership had always insisted they did not have."