Why do atoms stay nearer to each other even when delocalized electron moves away When the delocalized electron moves from between two atoms to other then why yet the measurement of distance between those older two atoms is less than normal single bond.
There is a significant quantum probability a delocalized electron is there, what in average attracts atoms together, compared to the state there was no such an electron. 

E.g. for benzene, the distance is shorter than for a single bond, but longer than for a double bond, being effectively 1.5 bond.