Windows Server 2008 onwards, last-access timestamp of log file is not getting updated after data insertion. Because updating the last-accessed timestamp requires writing data to the disk, an activity that accesses many files might be faster if this type of update is disabled. NtfsDisableLastAccessUpdate flag is enabled to disable the timestamp. 

You can follow below steps to enable last-accessed timestamp of the file. 
--> Press CTRL + R button on keyboard to open Run prompt.
--> type "regedit" in Input box.
--> Go to HKLM\SYSTEM\CurrentControlSet\Control\FileSystem
--> Check if "NtfsDisableLastAccessUpdate" flag is enabled with value 1.

Note: 1 - NTFS does not update the last-access timestamp of a file.
         0 - NTFS updates the last-accessed timestamp of a file.

--> Replace 1 with 0 and check if time stamp is updated or not.

Note: It is performance feature, so we should recommend user to contact their internal IT infrastructure team to check on this.

Related Articles on the web:
https://www.veritas.com/support/en_US/article.100023082
http://technet.microsoft.com/en-us/library/cc758569%28WS.10%29.aspx