Thanks so much for your cooperation and support throughout this process.
One of our devs has worked intensively on this and it looks like we have reached a conclusion to the cause of the issue.
The GoDaddy server goes to sleep after 30 seconds and when IWP tries to send a POST call, the server assumes that it is a malicious call and blocks the request.
This does not happen always but it does happen rarely. We have tried workarounds to trick the GoDaddy server into believing this is a valid call but we have not made any progress.
We would recommend you to move the WordPress site to a different server. Sorry to disappoint but this issue does not look like something that is troubling other IWP clients, it is troubling a lot of other applications too and the web is full of complaints about 408 issues with GoDaddy.
Thanks once again for patiently waiting for us to get back to you with a conclusion.