I checked the logs provided and can see the below lines :
00:0000:00000:00000:2016/06/17 22:38:16.33 kernel SySAM: Using licenses from: C:\Sybase\\SYSAM-2_0\licenses\SYBASE_ASE_DE.lic :
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: Checked out graced license for 1 ASE_CORE (2013.1108) will expire Sun Jul 17 22:33:17 2016.
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: Failed to obtain license(s) for ASE_CORE feature from license file(s) or server(s).
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: Licenses exist for ASE, but a license containing the configured (PE=EE;LT=AR) attributes could not be obtained. Verify that ASE is configured to use the correct type of license, and either reconfigure; or generate and deploy the desired license from the Sybase Product Download Center.
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: License feature name: ASE_CORE 00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: License search path: C:\Sybase\\SYSAM-2_0\licenses\SYBASE_ASE_DE.lic;
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: FLEXnet Licensing error:-73,125
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: For further information, refer to the Sybase Software Asset Management website at http://www.sybase.com/sysam
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel Error: 131274, Severity: 17, State: 1
00:0000:00000:00000:2016/06/17 22:38:16.41 kernel SySAM: WARNING: ASE will shutdown on Sun Jul 17 22:33:17 2016, unless a suitable ASE_CORE license is obtained before that date.
At present server is running in Grace mode and will expire after 30 days (On 17 Jul) . So You need to generate and apply the license file with PE=EE and LT=AR .
Gaurav