I'm an engineer and a soapmaker and I've made a lot of soap over the past 20+ years. In that time I have seen a number of problems with stick blenders and have found one that works for me (Hamilton Beach 2 Speed Hand Blender #59770). Unfortunately it isn't made any more. It isn't perfect, but does work well enough for production purposes for a few years before needing replacement.
I think I've replaced it every 4 years or so. Problems with it are the shaft and bell are plastic. They have cracked, or a seam has split. The seals around the shaft do wear too quickly, allowing air to be pulled in through the shaft to the bell. But mostly that the on off switch begins to fail and provide only intermittent contact and power to the motor. None of that is surprising because it's not an industrial tool, it's a home use tool. I work it much harder and more often than it was designed to do.
More important are the factors that make it a good tool for me. Mostly it's that even it's high speed setting is low enough powered that air bubbles aren't entrained into the soap. I have purchased and used perhaps 5 different makes and models of stick blender over 23 years, and most don't work well for soapmaking in my opinion. The biggest problem with them is that they have too much power. Too much power translates into too fast blade rotation and cavitation results leaving permanent bubbles in the soap. Every stick blender has the possibility of drawing air down the shaft to the bell. The more powerful the motor and higher the speed, I think the more likely that problem is. Sucking air into the soap also happens if the bell gets too close to the top of the soap in the pot, and the problem is worse with a more powerful motor and higher blade speed.
Overall, I think the most important issue for most soapers is motor power. Lower is better. Metal shaft vs. plastic shaft, shaft bearing quality, bell shape, bell perforations, seals, etc. I think matter less overall, especially if one makes smaller amounts of soap less frequently. I make nearly a ton of soap per year so I make my blender work hard.