Formal:
* N'abandonnez jamais. (This is the most literal translation and emphasizes the action of not giving up.)
* Ne cessez jamais. (This is a slightly more formal and poetic way to say "never quit".)
Informal:
* N'abandonne pas. (This is the informal version of "N'abandonnez jamais" and is used when speaking to one person.)
* Lâche pas l'affaire. (This is a common idiom meaning "don't give up".)
* Ne te décourage pas. (This means "don't get discouraged" and is a good way to encourage someone who is feeling down.)
The best way to choose the right phrase is to consider the situation and the person you are speaking to.