On small taps it is especially important to hold the tap holder in alignment with the drilled hole. Most tap holders have a center opposite the tap holding end. Lock the part to be drilled in a drill press or mill and drill the hole. While the part is still in the locked down position, tap the hole using a center, locked in the chuck and against the tap holder, following the tap down as it turns in. Most tap breakage comes from a side load and this eliminates that error. They do make a spring loaded tool for this, but I just follow the tap like I say above. I do many 4, 5, 6 as well as the regular 8 and 10’s we often use, and I don’t use anything special for taps just off the shelf brands but do replace them often.
Bob