There are a couple of potential causes for this.
1. The area hasn't been loaded
The requirements for grass to grow have, from your screenshots, all been met. There is enough light and grass around for the grass to spread naturally. Sometimes one or two blocks might be a bit defiant, and refuse to spread, but with the amount you have, this is unlikely. The only other thing is that the area needs to be loaded. Chunk Loading means that if you are not in the area (for example, you might be in the Nether), that area is not loaded - which means all activity stops. Your crops don't grow, sheep don't regrow their wool, and the grass does not spread.
2. The dirt blocks you are using are Coarse Dirt
Coarse Dirt was added in version 1.7, and is almost identical to normal dirt blocks, save for a mildly different pattern, and the fact that grass will not grow on these blocks. However, if you use a hoe on these blocks, it will change it into normal dirt blocks (Added in 1.8). Grass can then grow on these blocks.