Hello JPlante and welcome,
My guess is that it's a timing issue - Monarch can open 1024 reports at once, but if you're handling 1900, I suspect that Access was calling Monarch a few times the fetch the data. Is there a regular wildcard match to the filename so that you could join the text files together as one big report using a DOS command?
I was using in VBA in microsoft Access the method SetReportFile to open all the files one after the other and also using SetModelFile to open the model into which I was appending all the text files into a single table. I even try to put a deay of 0.1 sec in between the load of each text files. But now my biggest problem in that Monarch does not work anymore. It won't open nmay reports, even if I try to open a report manually.