What does 十天半月 (or 十天半个月) mean?
十天半月 or 十天半個月 means 十天～半個月 (10 days to half a month).

我長大以後喜歡往城裏跑，常常是十天半月不回家。
After I grew up, I loved going into the city, often not returning home for about a fortnight at a time.


For reference, both the Baidu Zhidao answers say approximately the same thing. 上中下旬 means the first, second, or third period of a month, with a period of a month being a 旬 (10 days).