I have four chairs on my patio/ deck that surround a glass table used for seating and entertaining company. On TWO of the chairs the strapping has worn thin over the years and has ripped. (You cannot see the rip in the photo because the rip is under the seat. Chairs are still very usable due to the strength of the strap design but both need to be repaired or replaced. 

My preference is to find someone who is skilled at this type of repair and has experience with indoor or outdoor furniture repair.