The answer to 'backflow preventer won't flush' is that a common cause is a clogged or stuck backflow preventer. This can be due to debris, mineral buildup, or mechanical issues with the internal components. Symptoms include the backflow preventer not flushing properly or not closing fully after use.
Some potential solutions include dismantling the backflow preventer, cleaning out any debris or buildup, and checking for any worn or damaged parts. However, this requires specialized knowledge and tools, so it's generally best to call a professional plumber to inspect and service the backflow preventer.