It sounds like the selection criterion is being "set" before the date value is populated on the first read but is retained when the report is closed and so becomes available for the second read.
From what you wrote ("Recently ...") should we assume that at some point in the past you did not have that problem with the process?
If so, what has changed?
That may be a tricky one to answer. I wonder if there might be a prerequisite process that could be applied in Data Pump to make sure the date is always available for the process. Doing that would be a more reliable and auditable way to ensure the automation is consistent in case there are timing issues of some sort running the rest of the process.
It would also be a safer way to great a process with some form of guaranteed continuity. There are times when sections of code are "re-purposed", often by the downstream developers of the development tools rather than the application coders, and one can end up with updates seemingly unrelated to an Application that result in things working differently to the way they used to work. Having specific steps in a process, as here with Data Pump, can help to eliminate such anomalies or at least isolate where they occur making problem analysis and rectification easier.
I have never had to deal with your specific problem. Hopefully someone who has worked out a practical solution for something similar will come along soon and offer more specific guidance.
Meanwhile I hope this gives you at least something to look into and would also suggest you check the log file to see if that offers any clues - you may already have done that of course.