Like Ming said "to maintain" is most appropriate meaning for 유지하다. When it's better (for stylistic purpose) to use "to keep", then the meaning is still same - "to maintain" or "to keep something in a certain state"
if you open endic.naver.com, search for 유지하다 and open 예문 더보기 then you can find many examples
모든 국가들과 우호 관계를 유지하다 = to maintain friendly relations with all countries
몸을 유지하는데는 적절한 영양 공급이 필요하다 = The body requires proper nutrition in order to maintain itself
"to keep doing something" you can also use 계속+Verb, I guess
비가 오후 내내 계속 내렸다 = The rain kept up all afternoon
there are many other verbs for "to keep" for each meaning of the verb
you can find all verbs that can mean "to keep" in endic.naver.com if you search for "keep"
(지니다, 지키다, 간직하다, 두다, 유지하다)
Good luck!