V-Brakes not sprinhing back
 

Just purchased a 2nd hand bike with V-brakes, the rear break goes on but when the handle is released, it doesn't go back and I can see the cable bunching in the middle of the bike. I tried lubricating the cable and tightening the springs on the v-brakes but still no success. The cable seems fairly loose so I don't think it's a blockage problem, the lever parts ( i don't know what they are called, the bits that move like pincers), are loose but don't separate when the brake is released.

There's a couple of possibilities:

The first one to check is the alignment of the pads with the rim. Take a close look at the pads. If they have a ridge at the bottom, the pad is catching on the inside of the rim. That's common as the pads wear. Resurface the pad flat with a fingernail emery board, raise the pad a few millimeters and you'll be good-to-go.

The second is return spring tension. Ussually (but not always) there are 3 little holes where the brake spring attaches to the bike. Figure out which one of those will increase the return spring tension. I mention this one last because, if it was ever right, it's unlikely to change by itself.

Or the brake cable could be hanging up in the housing.

The springs have to pull the cable back through the housing on return. If the cable is sticking, the arms can't return. Suspect this before a spring problem.

Another possible is the V-brake posts on the frame have gotten dry and need cleaned and regreased. bk

Maybes theres cable problems.
check that the cable stops on the frame have no damage and the slots are straight. The stops can get knocked and close up and jam the cable a bit. try levering the slots with a flat screwdriver.
the ferrules that go on the end of the cable. check that they are undamaged. you can get new ones from a bike shop.
check the cables have no splits on the plastic coating. This could lead to water entering and making it rusty inside. also would make the cable less smooth.
check that the brake noodle is ok. This is the metal curved tube at the end of the cable on the brake caliper. If this has dents in it. That will jam the cable. If its a flexible one, like a bit of brake cable. There hopeless. I would replace it. Theres 2 different types. 90 degrees and 135 degrees. get the angle that matches what youve got