Unable to import large document during cron

I have a regular import configured. If I go to http://site.domain.tld/import/spectrum_data I will see that it thinks the import process is 95% complete. If I go to the server and run cron, I see this:

fopen(public://feeds/FeedsHTTPFetcherResult1374609001_1): failed to open stream: "DrupalPublicStreamWrapper::stream_open" call failed FeedsFetcher.inc:92    [warning]
fgets() expects parameter 1 to be resource, boolean given FeedsFetcher.inc:93    [warning]
fclose() expects parameter 1 to be resource, boolean given FeedsFetcher.inc:94    [warning]
fopen(public://feeds/FeedsHTTPFetcherResult1374609001_1): failed to open stream: "DrupalPublicStreamWrapper::stream_open" call failed ParserCSV.inc:21    [warning]
Invalid argument supplied for foreach() feeds_tamper.module:47    [warning]
PHP Fatal error:  Call to a member function shiftItem() on a non-object in /var/www/drupal7/sites/sites.domain.tld/modules/feeds/plugins/FeedsProcessor.inc on line 180

Fatal error: Call to a member function shiftItem() on a non-object in /var/www/drupal7/sites/sites.domain.tld/modules/feeds/plugins/FeedsProcessor.inc on line 180
Drush command terminated abnormally due to an unrecoverable error.    [error]
Error: Call to a member function shiftItem() on a non-object in /var/www/drupal7/sites/sites.domain.tld/modules/feeds/plugins/FeedsProcessor.inc, line 180

As it says, feeds/FeedsHTTPFetcherResult1374609001_1 does not exist.

It seems like the process in cron is deleting the files that it needs before finishing the import.

I also seem to have 38 of >2,000 items changed on every import, but I know for a fact that the document only changes 2x/day so there's no way 38 items are being changed on every import. Something is going on there.

I don't have this issue on other websites where the csv file that I'm importing is small, but do on this site.