SSIS hangs during For Each File enumeration
This appears to be an issue with the Visual Studio / BIDS client hitting memory boundaries, not with SSIS itself. While the package is running in debug mode in BIDS, the devenv.exe process can be observed to continually occupy additional memory. While the number of files processed before hanging is inconsistent, the package did, on one occasion, process nearly 9000 files before Visual Studio threw an out of memory exception.

Running the package with dtexec or through SQL Agent appears to resolve the issue.