We usually use the verb 持续 in the following set expressions:
持续下降 持续发展 持续作用 持续改变 持续下去
The verb 延续
We also use the verb 延续 to indicate the continuation of something without interruption, but it’s mostly used with abstract objects.
For example, objects such as “dream”, “life”, “traditions”.
Examples
中国的历史延续了五千年
China's history extends over 5,000 years
zhōngguó de lìshǐ yánxù le wǔqiān nián
这是一个将要延续多年的糟糕困境
This is a bad problem that will last for years
zhè shì yí ge jiāngyào yánxù duōnián de zāogāo kùnjìng
地球上的生命将无法延续,除非人口增长得到控制
Life on Earth will not continue unless population growth is controlled