Literally 'dry-stare-eye': you stare so hard your eyes go dry, but you still can't change the situation. The 干 here means 'futile, in vain' (same usage as in 干着急 gān zháojí, 'fret in vain').
culture
Also the name of a fast-paced shedding card game popular in northern China — players race to empty their hand and the loser literally sits there 'staring helplessly'.
