Replacing your time with one here which should trigger the if branch (rather than the else) I am unable to reproduce your findings.

$ perl 1178137.pl 
The current time is Mon Dec 19 23:40:37 2016
The old time is Mon Dec 19 23:31:00 2016
Half an hour ago is Mon Dec 19 23:10:37 2016
Old time is within a half hour

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If you think you have timezone (or DST) problems it is always best to output the epoch times as a diagnostic aid. I suggest you give that a try.

In reply to Re: Simple (I thought) time comparison? by hippo
in thread Simple (I thought) time comparison? by sjessie

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