The logs get over-written depending upon the app usage. If you want to increase the number of files created for serverout logs, you may edit the logging.xml file (ManageEngine\SupportCenter\server\default\conf) and make the change like explained below.

<FileHandler append="true" archivedirectory="log/archive" filecount="10" filepattern="serverout%g.txt" archivestatus="false" logdirectory="log" maxlimit="10000000"/>

By default, the filecount is 10, you may increase the count so that, the specified number of files will be created as serverout logs, by this you may avoid the logs by getting overwritten.

PS : Take a copy of the file before making any change.