Why is SSIS slow to enumerate over many files in a directory and import them?

Question

I have a terribly slow SSIS package. It's quite fast with one file, and reasonably fast with 100 files or fewer. (About one second per file)

However, if my directory has thousands of (very small) files, the process drags on terribly slowly. My preference is to run this process only after business hours, but by waiting until then, the number of flat files to import is in the thousands.

The package is very simple:

• Outer Loop is For Every (file enumeration, read file path into variable)
• Inside, simply import without any transformation to the data

That is it.

Performance with thousands of files is running 15 seconds or more per each file. The UI (status) is drawing/scrolling so slowly that I can't even see where it's at -- the stamped time is more than 15 hours old on an execution that was started 18 hours ago.

Version: MSSQL 2012