I totally agree with Todd. Most big box tap and die sets are carbon steel and they work ... just maybe not for long. A HSS set is the way to go but a new set is big bucks!
Just about everyone who makes taps also makes HSS dies - Irwin-Hanson, Greenfield, Cleveland, Titex, OSG, Gurhing, etc. Some of them make cobalt dies and price them accordingly.
I have a HSS Irwin-Hanson set that cost way more than the carbon steel one and it works well. It is my "use it first" set and has lasted many years.
The older Crafstman Kromedge tap and die sets were HSS but you can only get them on ebay. These were actually very good sets that lasted for many years when used properly. If you watch for it, you can get a good set there for a decent price. Try to find a set that wasn't used too much; hopefully the seller will be honest about it.
I also have a full set of Imperial adjustable button dies up to 1/2" that is used in my tailstock die holder for use on the lathe. If I could only have one set, it would be this set. These have a split on one side of the die that allows you to adjust the fit of the thread; its finicky but sometimes it can save your butt. Good to have but these are the highest in cost. Cobalt is even more!
Rather than buy a full set, which costs a lot of money, you can buy individual HSS dies as Todd suggests. It is more economical and over time you will accumulate what you need. Maybe replace that one that messed up your rod for now and wait for a Kromedge set?