How important is it to continue to take foreign language in HS after finishing requirement?

That statement is not correct. If a college requests 4 years, and a student has completed level 4 in 2 years, as an example, then the recommendation is met for 99%+ of colleges. For more discussion, see:
http://talk.collegeconfidential.com/college-admissions/1802227-faq-foreign-language.html#latest

Top colleges may ask for 3-4 years of foreign language study in HS (or completion of level 3-4), regardless of HS graduation requirements. Most colleges outside of the top will only want 2. So, part of your answer depends upon the colleges DD is targeting. If DD is planning on applying to a college without the minimum recommendations, that does not mean that the application will be trashed automatically, but the vast majority of applicants will have completed them.

Also be aware that many colleges have a foreign language requirement for graduation. So the more one takes in HS, the (theoretically) fewer one needs to take in college.