keep doing sth.保持做...

而look up的意思有：

向上看; 抬头看

Don't look up.

不要向上看。

改善; 好转

Business is looking up.

商业日趋繁荣。

拜访(某人)

Next time you are in Beijing, look me up.

你下次来北京时, 来找我。

所以整个句子翻译下来就是：保持情况好转。