Two senses: (1) the figurative 'crestfallen / shamed / defeated' use is far more common in modern speech, almost always paired with verbs of leaving — 灰溜溜地走 / 灰溜溜地跑回家; (2) literal 'dingy gray' for a drab color or old surface.
memory
Pattern: adjective + reduplicated suffix (XYY). 灰 (gray) + 溜溜 (slipping/sliding) — the slinking-away image fits perfectly: someone the colour of failure, slipping out of sight.
