Are you talking about LeakyReLU by chance and not ReLU? Because ReLU is known for vanishing gradients, since any values less than zero are mapped to zero. This is true regardless of the number of layers. LeakyReLU on the other hand, maps the values less than zeros to a very small positive number. This prevents vanishing gradient from occurring.
EDIT: LeakyReLU prevents dying ReLU from occurring not vanishing gradient. PReLU prevents vanishing gradient from occurring.
EDIT 2: To answer the comments. VGG was proposed in the paper "Very Deep Convolutional Networks for Large-Scale Image Recognition" and was one of the top performance models for the ImageNet challenge at its time. Architecture wise, VGG wasn't completely different from what was done in the past. However, it was much deeper. This is impart where the vanishing gradient becomes a problem. It does not really have to do with ReLU alone but a combination of every single layer.
Enter ResNet, which uses skip connections. These actually make parts of the networks shallow and makes it easier for the network to learn both easy and difficult tasks (ie. low and high frequencies in images). More difficult tasks require more learnable parameters while easier tasks require fewer parameters.
I believe PReLU being a learnable activation function can help deal with this task.