let's still in contact with each other 是病句吗

是病句。

let引导的祈使句，后面的's代表的是 us
即let us do...
此句展开后缺少谓语

正确的是 let us still keep/be in contact with each other.

有点毛病，应该加个Be动词。let's still be in contact with each other.
因为保持联系是 be in contact with sb

很明显啊，连谓语动词都没有
如果是保持联系的意思的话用keep contact with

Keep in touch就好了。。。in contact with each other 好长好罗嗦呀。