Getting soft 404 errors (200 status) when caching plugins are enabled

W3 Total Cache has the following option that if enabled will cause this behavior:

Cache 404 (not found) pages

Reduce server load by caching 404 pages. If the disk enhanced method of disk caching is used, 404 pages will be returned with a 200 response code. Use at your own risk.

Other caching plugins may have similar functionality.