If your snowshoes are 18 years old and the material became brittle then it seems quite likely that you might experience similar problem in other parts of the snowshoe that uses the same type of material (perhaps just on the other snowshoe.) While I generally prefer to repair things rather than throw the away I think at some point you need to evaluate if it is really worth fixing and what is the risk if, for example, you experienced another failure on the trail? If it can be remediated with a simple field repair then perhaps trying to repair is the way to go, but if the failure on the trail is non-trivial then maybe a new pair of snowshoes is the right choice to make.
I don't have Atlas snowshoes - I have Tubbs and I had to repair them once when I accidentally ripped out a rivet when stepping over a fallen tree. I contacted Tubbs, sent them a picture and they sent me a few rivets which I used to repair myself as I did not want to send my snowshoes for a fix that I deemed pretty simple.