As the Gang of Four book says, you should "favor 'object composition' over 'class inheritance'." So rather than creating mixins, you should usually create objects that are comprised of several smaller objects which operate independently.
There are a lot of reasons for this. The first and most obvious reason is that it makes unit testing a lot easier. If I have a class which inherits from 3 other classes, I can't test that class without also testing the three base classes. I may not even be able to construct an instance of that class without providing a lot of irrelevant inputs-- file descriptors to open, memory to allocate, and so forth. On the other hand, it's easy to create an instance of a component and test just that component.
You can get around some of these problems by constructing "mock ups" of some of your class components. You see this a lot in Java code. But it's difficult, and even when executed successfully, it bloats the code.
Creating elaborate and deep inheritance hierarchies increases compile time and the coupling between components. The former chews up machine cycles when compiling (at least if you're using C++). The latter chews up human time when trying to maintain the code, no matter what language you're using.