require/include fails with APC enabled

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I have one server that is acting up whenever I try to enable APC. PHP
scripts execute normally as long as there are no calls to include(),
include_once(), require(), or require_once().
Any file (no matter the size) that can be included while APC is disabled
will cause the script to silently fail at the point of include when APC is
enabled. There is no output in the PHP error_log, even when logging all
message types.

This feels like it's probably a really simple fix, but we're stumped. Any
help you can provide would be greatly appreciated.

Server software combinations:
PHP 5.2.9 with APC 3.0.18 and ZTS
PHP 5.2.6+lenny3 with APC 3.1.2
PHP 5.2.6+lenny3 with APC 3.0.18

Apache 2.2.9 in all cases
APC is configured for pthread mutex locks. mmap disabled.

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