Normally if a connection is blocked by an F5 security product and HTTP is involved a 200 OK with an error code via the body is presented and a connection is not simply dropped so I would recommend a packet capture to validate where the TCP connection is dropped.
PURGE and PURGE_URL are non standard HTTP methods and are not listed in any RFC. If the TCP connection being dropped by BIG-IP there is a virtual server processing the traffic that has an HTTP security profile applied to it and the methods in question are not on the allowed list via a custom method.
I took a quick look at an HTTP protocol security profile in AFM which shows that PURGE and PURGE_URL are not in our standard list of methods. To allow them one needs to explicitly create them via Security --> Security Profiles --> HTTP. The exact details of the configuration will vary based on how the system is setup and the documentation on the product. I recommend a case be opened to further investigate the config setting you need since DDoS hybrid defender also has wizards that may obfuscate the setting or require other settings be touched.