The phrase "continuous rain" is perfectly acceptable in written English.
You can use it whenever you need to reference a long duration of rainfall. For example, "The region experienced continuous rain for several days, causing widespread flooding."
"Just continuous rain, not having an opportunity to plant.
Because I drove it during a weekend of continuous rain, the roof never came down.
"Nimbostratus are a thick, dark grey layer that produces continuous rain or snow".
At the beginning of August 2006, a fortnight before our arrival, Ladakh had been lashed by eight days' continuous rain.
In spring 1998, heavy and continuous rain made it look for a time as if the vines would never flower, which meant that many grapes would never ripen.
As 1999 drew to a close, two weeks of continuous rain drummed down the sides of the Ávila Mountains in northern Venezuela.
Continuous rains plagued the workers and caused the flood waters to rise higher.
Excessive and continuous rains this year have delayed the harvests of cotton, and with the recent cyclone it is expected that there might be another spell of rains here.
The few who started farming had also substantial harvests which sometimes rotted in the fields due to continuous rains".
In the Philippines, six people were killed in flash floods after continuous rains in the area caused local rivers to overflow.
The evidence for this is reflected in the responses of the farmers: most of the interviewees reported highest yield in 2010, and lowest yield in 2003 when continuous rains during the winter wheat ripe period affected the growth of the crop, resulting in great decline in yields.
