When you have a lot of them, say when you first arrive in a chaotic environment
a weekly meeting will get support.
When things are somewhat improved and CARs are exceptions rather than daily activities, then it can be a challenge to get the persons tasked with correction and corrective action to get off their butts and do the job. Especially if it's not a priority for their boss.
You can help by carrying as much of the load as you can - if a document requires an update or creation, offer to interview the owners and do the writing yourself, enlisting them for review and approval.
Keeping CARs in the public eye helps - I have experimented with mandatory closure timeframes, which proved unenforceable, and sometimes impossible due to the nature of the product line (can't prove it worked until we run that product again). So I steered away from deadlines and got spanked by an external auditor for ineffective process when a CAR went dead in the water (too long a story, let's just say management learned a lesson) so now I have to review CAR closure time spans in monthly KPI meetings.
It's a common problem, based around insufficient management support for the process.
Hell, I have resorted to spamming the CAR owner with a string of emails " Hot Russian Girls Want You To Close CAR 1047 " - " Help me get $10,000,000 into the USA via CAR 1047 " and graffiti (simulated military recruiting posters in the bathroom, lunchroom and halls with a picture of Uncle Sam captioned with Uncle Sam wants you to close CAR 1047 ". I have gotten people pissed off at me and complaining to my boss.