E. coli not growing in liquid medium
I think there is more than one possibility for this.


Plates bearing colonies are stored for too long in 4C(as @mdperry suggested). This causes the colonies to lose the plasmid over-time as the antibiotic in the plate gets degraded over-time. There is a study on this and I've shared the link. (http://homepages.bw.edu/~mbumbuli/biotech/colin/index.html). 
The insert is toxic to cells and promoter is not strong enough. There is a leaky expression causing cells to die.
Check the competent cells and their storage condition as it would greatly affect the efficiency of transformation. Do a mock transformation with plain plasmid without insert and spread them on an antibiotic plate.