Amazon RDS Instance slowly losing free diskspace

You can check your binary log retention period by the following command under MySQL:

mysql> call mysql.rds_show_configuration;

To set the retention period to 1 day, use the command:

mysql> call mysql.rds_set_configuration('binlog retention hours', 24);

Which means MySQL servce will purge binary log every day.

Besides, the binary log, I think you can check the setting of innodb_file_per_table, all data will be stored to ibdata file if it is assigned with "0".

I suggest you to assign the option to "1" so your table will be stored separately and you can reclaim your used space by:

mysql> OPTIMIZE TABLE <table_name>

Check the reference links below to see if they reflect your problem:
How to reclaim space in InnoDB when innodb_file_per_table is ON

Why is the ibdata1 file continuously growing in MySQL?

One more thing, according to the website, you will have fast growing ibdata1 file because you have long running transaction. Try to commit them as soon as possible to avoid performing system restore to reclaim space.