Mail queue in JIRA 5.2 flushes at a rate of one message every 33 seconds. In busy days, some messages are actually sent hours after they were generated.
If, while flushing, I send a test message from JIRA Administration (that appears not to go through the queue) it is sent straight away without affecting the slow flow of the queue. That facts makes me think that the problem is not on the mail relay server.
There are a few reasons for this problem. I would recommend you to review this guide:
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