。
Don't lose heart — keep writing steadily.
Literal
Courage [object-を] not-losing steadily write-continue-[imperative-なさい].
どんどん is a 擬態語 for steady, vigorous progress — things moving forward without hesitation. 失わないで ('without losing') uses the negative te-form to maintain a condition while the main action proceeds. 書き続ける chains 書く with 続ける ('continue').