。
A busy bee has no time to be sad.
Literal
Busy bee [topic-は] grieving time [subject-が] doesn't-exist.
An aphoristic sentence — the 'busy bee' trope exists in both English and Japanese. 悲しんでいる暇がない uses a relative clause (悲しんでいる modifying 暇) inside the ~暇がない pattern. The ている marks ongoing state within the relative clause. Reads more like a translated proverb than native Japanese idiom, hence the lower naturalness.