First, I wouldn't ever recommend, nor do I think a manufacturer would either, using a rod to pull a snag free. First try giving the snag a slight wiggle with the fly line, or pull directly on the line, but don't use the rod as a lever. It's very easy to bend the rod in unnatural ways that can weaken the structural integrity of the graphite. This may have resulted in your first tip break.
Also, think about the history of your usage of that rod. Have you ever stuck the blank with any weight or weighted flies while casting, knocked it agains a tree or brush while hiking to or from a fishing spot, landed a fish with the rod tip pointing up and away from the fish, gotten snagged on a tree or bush during the backcast and continued the casting stroke after you felt the snag (very hard not to do in my experience), or had a knot from the line/leader connection get snagged on the tip guide of the rod while you pull on the tippet end. Any thing that could have smacked the blank, or caused a stress point in a specific location can cause a rod to break down the line. A rod is designed to have stress distributed along its length, anytime this stress is concentrated, there is potential for breakage, either now or later.
And, yes, faster rods are a bit more susceptible to these issues, in my opinion. They are generally made from higher modulus graphite, thus making them a bit more brittle and delicate.
Dead fish don't make reel music.