When I'm going to prepare my parents' 3rd visa application. The agency told me only apply one of them since we have two refused records. But my husband and my friends all suggest to apply both of them. The situation to let VO judge if parents will back to China before the authorized stay is your tie with China. We submit 3 letters, invitation letter/ letter to VO from applicants/ letter to VO from inviters, we spend lots of time on revising these letters. Also, the MP office write a support letter which indicate applicants' situation and inviters' significant changes this year. My suggestion is you can find your MP in your area and let them send email to Beijing/Shanghai Visa office, and you can get the real refusal reason. Your MP office also can help you write a support letter. Good Luck to you!
*sorry, I couldn't type Chinese on my office computer"