They would most likely need to replace the fabric. It can be done. I think I have the lounge chairs in the same style.
You may want to call Bunchers Hardware in Millburn. They used to do some patio chair repairs, although I don't know if they still do and if they do, they do what you want.
John Dilly at Bee and Thistle does some chair repair. It wouldn't hurt to ask him.
If it helps anyone, these web sites offer repair of patio furniture: www.casualfurnitureservices.com , chaircarepatio.com and gardenwinds.com
Promote your business here - Businesses get highlighted throughout the site and you can add a deal.
We bought these Agio patio chairs at the Fortunoff outlet on Rt 22 a few years ago. They are super comfortable but pricey. They're starting to rip as shown in the pic. Does anyone know of any place that repairs these?