Why do teachers not participate in research?
The question asks why "teachers" do not participate in research, however it does not specify if primary, secondary, or higher education teachers are the focus of this question. The answer is that teachers at all levels participate in research.
Teachers in higher education frequently participate in research as part of their employment with universities. Part of their job is to preform research and to publish in scholarly journals. These teachers focus their research on their particular field and this research may or may not be student or learning focused.
Teachers in secondary education are not often required to complete research as part of their job description, however this can still happen as part of their professional development. Often at the secondary education level the research is student focused on topics such as student learning or classroom management.