I am fighting that battle right now. Over the last 2 yrs several audits called attention to our lacking CAR process, so we started taking steps to improve, including 2nd-party review of CA responses (for robustness). I don;t like it but right now in my org, its necessary. Last Aug, my CEO asked me to begin putting out a weekly Open CAR report to all senior management. Brought a little more visibility, especially when the CEO questions those who's reports have open CARs...but that doesn't always happen; there are bigger fish the CEO has to fry most weeks. Around Feb we adopted a 7D process (for simplicity's sake) for all CAs and shortened CAR reponse & implementation to 30 days. We have as many open CARs now as we ever did and what is more frustrating is the terrible actions given that are supposed to solve these problems (yes, from people with the word "Manager" in their title)! How in the world do you make Manager and you cannot solve simple problems...but i digress.
We did a little interviewing around the org to get feedback why CARs were not getting solved in a timely manner. The top things mentioned were:
1. Lack of training in problem solving/root cause analysis (some have had it before but still...common sense to most of us but worth thinking about).
2. Lack of accountability/lack of urgency from those that own CARs and their management to deal with them and not ignore them. Spending time on "getting the order" is waaaay more important than time spent fixing problems.
3. Assigning CARs to the wrong personnel; those that don't have training (we actually had managers delegate their CARs to low level personnel who had no clue how to answer them). Ridiculous but it was happening!
4. (from me) as you can see, the above 3 are byproducts of a weak QMS--a fairly hairy problem by itself because it requires culture change to correct, which is always a big deal. If the org doesn't understand what CARs and continuous improvement give...you're starting in the basement.
We're inching along making some progress but its painful. Among other things, we are planning some problem-solving training and I "coach" all levels of personnel almost daily on appropriate CA responses & how to solve their problems (I have asked for a bigger check since I am solving people's problems for them)! We are replacing our Word "CAR form", which is emailed around, etc, by having IT build a SQL CAR database to handle inputs from all associated parties, with built-in automated alerts, etc. We hope this will speed up the logistics somewhat. If you check around though, probably the heart of your problem lies with some of the things i've mentioned above.