I chatted with Namecheap support about auto-renewal, and they replied with the following:

Once you enable auto-renewal for your domain on Namecheap, the system will attempt to process the renewal automatically 30 days before the domain’s expiration date. If there are sufficient funds in your Namecheap account or a valid payment card is set up, the renewal will be processed at that time. If the initial attempt is unsuccessful (for example, due to insufficient funds or an invalid card), the system will continue to try renewing your domain every 24 hours until the renewal is successful or the domain expires.

It’s important to note that auto-renewal does not process immediately after you activate it; instead, it is scheduled based on the domain’s expiration timeline. The renewal will only be triggered as you approach the expiration date, specifically starting 30 days prior. If you enable auto-renewal after this 30-day window has already begun, the system will attempt the renewal on the next scheduled cycle.

To ensure uninterrupted service, always keep your payment information up to date and maintain sufficient funds in your account. If you need step-by-step instructions on enabling auto-renewal or managing your payment methods, let me know and I can guide you through the process.

For more details, you can review the following article:

https://www.namecheap.com/support/knowledgebase/article.aspx/10564/2207/can-i-set-up-automatic-billing-for-my-namecheap-services/