Files already on the Hitlist / Blocklist are not automatically deleted as expected. There is no error.

Confirm in File Slayer Setup that the object the file is related to is enabled. Case and Email Message are most common.

Confirm that the file you expect to be deleted and the file on Hitlist / Blocklist, are indeed the same. The true determinant is whether the checksums match, but it's easier for most to compare the file size. If the byte count of the 2 files are identical, it is extremely likely the checksums will match and they are the same. The file names are irrelevant.

If using Email to Case or Email to Case Premium confirm the owner of the case is assigned a File Slayer license

For Email to Case Premium (E2CP):

Navigate to the Email to Case Premium Setup, from the "Global" tab, click on the user for E2CP Context User.

Confirm that this user is assigned:

• A File Slayer license
• Read on the Documents object. We recommend using a permission set.

For Email-to-Case (standard):

Navigate to Salesforce Setup > Support Settings, and check the Automated Case User.

If the Automated Case User is System, it cannot be assigned licenses. A real Salesforce user is required:

• You can use a standard user license, but it's more cost effective to use a Salesforce Integration license. These permissions are intended for Email to Case Premium, but can be applied to OotB Email-to-Case standard. 
• The System user has fixed System Administrator permissions, and using a real Salesforce user requires the same. Email-to-Case standard requires sweeping access all of your data. Assign the System Administrator profile if using a standard user license, or for Integration licenses, create and assign a permission set with Modify All Data and Send Email permissions. See Salesforce KBA "Details on Automated Case User". If following the principle of least privilege is important to your organization, consider Email to Case Premium.
• Update the Automated Case User in Support Settings.
• Verify the user’s email address

Confirm that this user is assigned:

• A File Slayer license
• The expansive permissions required by Email-to-Case (standard) already include access to the Documents folder

Notes: 

We do recommend using the Salesforce Integration User license which provides access to Salesforce data and features exclusively through the API. If you're not using the Salesforce Integration User license for the Context User, we recommend using a dedicated automated user with the System Administrator profile. Assigning a unique user to each integration helps isolate access to specific data sets, offering greater control and improved traceability of transactions across integration points.