What to look for in a hand mixer for occasional bread dough kneading?
That particular style of handmixer you've been using is not really used in the pro or semi-pro (this is why rumtscho says there is nothing).  The main reason is the torque gets translated into wrecking your wrist.  Dough has a very high viscosity and it is a non-newtonian fluid which can make mixing with a handheld machine a frustration chanllenge.

Simply put, a hand mixer is just not the right tool for making dough.


To make dough, you're better off with a stand mixer (like a kitchenaid artisan or pro).  For larger batches you'd need a bigger mixer (planetary or spiral) like a Hobart.   They  get bigger from there (met a baker in Pittsburgh that worked with a mixer-motor made by Harley Davidson).

Most pros use the vertical type handheld mixers (they look like immersion blenders)

 

They're referred to as hand-held mixers, power mixers, immersion blenders, or in some kitchens "boat motor".  But they are not made for making dough.  They will do the blend and mix cream part and are almost indestructible with mostly stainless steel parts. Your local restaurant supply dealer should have the category. Some brands are: Thunderbird , Robot Coupe, and Dynamic.

That is to strictly answer your question regarding new model, more robust, less plastic, semi-professional part.

However, if that's overkill for the once every two weeks, and a stand-mixer is not in the cards, I'd recommend the 9-speed Kitchenaid:

 

These have two important features for dough making:


Mixing Load Sensor should prevent those runaway mix speeds and help protect the motor from burning.
The shape of the dough hook is not a corkscrew.  This seems quite clever. They have mixed the spiral direction of the hooks to reduce the corkscrew-effect and the dough-shoot-effect you might have experienced.


Finally, if you are going to be using this kind of tool, try to pay attention to your biomechanics.  Operating them with off-angles of your wrist and elbow could place undue pressure on the joints.  If you find that you're fighting with the machine, stop and kneed by hand the rest of the way.  The strech and fold technique is quick and easy as illustrated by Richard Bertinet in this video.