For all of you late Adopters of the PS VITA, here is the Perfect solution to the Download issue you were facing.

Basically the Backgrounds Downloads of the content downloaded off the Vita PSN Store stops downloading if the Vita is Manually made to Sleep.
The Right way to make downloads in the Background is to tweak the Power save settings of the Vita so that it goes to a Pseudo-sleep state(much like a Suspended animation, in medical terms) wherein thebodily functions of the Vita(the Background downloads) definitely work though there won’t be a pulse (Lit screen).

After the Downloads are started just leave the Vita alone for like a Minute or so untouched and Bingo the Downloads won’t be interrupted like before.