We have an issue when trying to create a PDF with a large JSON. The process works fine with 8MB of data in the JSON, but when trying to create a PDF with 16MB of data it will fail with "WebMap_as_JSON is empty. Web map has invalid JSON. Failed to execute (Export Web Map)". The custom print service is on an ArcGIS Enterprise Server running 11.1. I looked through the posts and did not see anything that deals with data size when having issues with the Custom Print Service.
I've had a colleague struggle with something similar in the past. He ended up changing the service from synchronous to asynchronous in Server Manager and the service began handling larger print jobs much better. Dunno if that was really the "right" fix or not, but it worked in his case.
I did try both synchronous and asynchronous, the user had no change in the error message received. Unfortunately, that did not help us.
Hey Pat
It might also be worth checking the version of ArcGIS Pro that was used to publish the custom print service.
The following documentation goes into further detail on this.
Hope that helps,
David