It's very sad when you're carried away weaving and wire broke suddenly or over. I recommend to remake this place completely - it will be reliable. But if it is difficult and you will certainly want to continue - you can take an extra piece of wire and weave on. In this video I show how you can connect the two pieces of wire. Such connection better make at point where the item will no affected of tension and friction.
Sometimes i leave the wire and looking for a new craft. Yesterday I began to sew a new handy bag for myself! Old sewing machine of my grandmother helps me - it is manually operated, not very comfortable. As my grandmother used it?! )))