可以说continue for 与continue to都不是固定搭配（不属于词组或短语）。
continue for 是持续或者继续多久的意思,for是介词，
The king decided to continue him for another term.
国王决定让他再留任一届。
The rain have continued for two days.
雨连续下了两天了。
Wet weather may continue for a few more days.
多雨的天气可能还要持续好几天。
continue to中的to接动词原形组成不定式。
Continue to listen attentively to sb
继续留心地听某人说话
He continues to do it.
他继续做它。