Couple things I’d try:
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I’ve seen weird behavior with plugins in general when WP isn’t given enough memory. You might want to up PHP and WordPress’ memory limit and see if you still get that weird behavior.
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WP Cron only runs on a page load so between 4:05 and 4:07 (or whenever you’re getting the weird behavior), check your server’s access and error logs and see what else might be hitting it in the mean time or if WP is failing somehow.
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You might alo want to try a plugin like WP Crontrol and see what else might be firing during that time.