That hurts..especially with the high prices they’re getting for pocket watch mainsprings these days! I’m assuming you’re talking about a pocket watch mainspring.
They really shouldn’t break off that easily so I’m wondering if you may be using older springs. You’ll often find that the older springs like “Black Shield” sometimes become very brittle over the years. If that’s what you’re using and the spring has become brittle then there’s no use trying to repair it as it likely will give you more problems in the future. These older springs were made from carbon steel alloys which degraded over time. Somewhere around the mid 1940s they started improving them by using other alloys. When given a choice I always buy these springs. “White Alloy” is a name you’ll see around quite often and are far superior to the earlier types. They not only withstand tension much better but are also stainless (I think) and don’t tend to rust or “set” like the earlier springs. By the 1960s the springs were improved so much over the older type that breakage under normal winding and running rarely occurs as compared to the carbon steel springs.
The high carbon springs are dark blue in color and have been hardened and tempered to that blue color. To rivet them you can anneal the end to be riveted, then stack and drill the mainspring end and the piece to be riveted together. By annealing you can sometimes fold the end back over itself and then drill through both pieces with a spade drill (or twist drill if you have one) at the same time. It’s just my opinion but repairing a high carbon watch spring isn’t the way to go if you have an alternative such as getting a newer White Metal spring….but that may not always be an option when dealing with pocket watches.
Keep having fun!