I have my coop in a permanent position with a large penned area (roughly 30ft square). Eventually the grass does start looking very sorry for itself due to all the scratching and droppings.
In order to allow my hens access to a constant supply of luscious green grass I either cordon off a section to allow parts of the pen to recover or I let them out of the pen altogether. Chickens know to get themselves back to the coop when it begins to go dark.
From time to time I sow some purslane, dandelion and clover seed to add a bit of variety for my girls. With the introduction of purslane to a chickens diet increases the amount of Omega 3 in their eggs.