To continue on means: carry on with, resume, pick up, keep up, keep at it, stay with, stick with one’s guns, extend, hold on, prevail, subsist, live on, keep going, endure, sustain, maintain, prolong, recommence, push on with, not give up, get on with, never cease, not stop doing something, to go on, to keep living, to survive.
Namaste, my friends