For instance, let's suppone we are walking for a long time and I have need to rest, i could suggest: " Facciamo una pausa! "
let's have rest! ==> facciamo una pausa!
But we are really close home so in this case you could answer: "Continuiamo" or "Resisti!" "Fra 5 minuti saremo a casa!" or "Ancora 5 minuti e saremo a casa")
Keep on ==> continuare, resistere
In this context "perseverare" is not used, it is more suitable for longer-term goals. But if you use it, we can understand the meaning anyway!