Can I schedule an RDS Reserved Instance renewal in advance?

There is no auto renew mechanism as far as I know.

On FAQ: https://www.amazonaws.cn/en/rds/faqs/

When your reservation term expires, your reserved instance will revert to the appropriate On-Demand hourly usage rate for your DB instance class and Region.

Hinting that you then must renew manually after it. Look at this to then act: https://repost.aws/questions/QUe1rs6x8dTbG42iEACqF47w/how-can-i-convert-my-on-demand-rds-db-instance-to-reserved-rds-db-instance

This knowledge doc talks about EC2, but you would hope the process for RDS is very similar https://repost.aws/knowledge-center/renew-ri

To renew your EC2 RI automatically, you can queue an RI purchase for the date and time that your existing RI expires. On the scheduled date and time, AWS automatically purchases the RI for you using your account's default payment method. For more information, see Queuing your purchase.