From Merriam-Webster

Synonym Discussion: continuous, constant, incessant, unremitting, perpetual, perennial:

continual and continuous indicate lasting occurrence or presence over long periods

<we live in a country where his Majesty's Cabinet governs subject to the continual superintendence, correction, and authority of Parliament — Sir Winston Churchill>
<the new struggle was continuous, the old had been sporadic — Lewis Mumford>

continual is somewhat more common than continuous in describing intermittent action, but both words are well-established and satisfactory in this sense

<the century and a half that followed the gathering of the estates at Westminster was a time of almost continual war — J.R.Green>
<continual and regular impulses of pleasurable surprise from the metrical arrangement — William Wordsworth>
<continuous landslides raised the cost of maintenance so high that a loss was sustained each year — American Guide Series: Connecticut>

Unlike continual in this respect, continuous may apply to space as well as time

<the continuous plains of the Great Lowland overlap from the Continental and Arctic drainage of the Heartland into the east of the European peninsula — H.J.Mackinder>