There would have option to preserve the svn history log while importing repository or svn check out the repository.
As we need to move current svn repository server to Atlassian (On Demand) - Fish eye repository But, not able to find any interface which can allows to preserve the SVN LOG history.
Developer: Atlassian Software Systems
Plugin key: com.atlassian.jirafisheyeplugin
Provides OnDemand-specific capabilities to the original JIRA FishEye plugin.
Plugin key: com.atlassian.ondemand.backupmanager.on
You take a dump of your old repository and you can import that. Please be aware Atlassian has announced dropping support for subversion as I read things. You can find the url about the end of life also in the same url about importing data.
Fisheye is not a subversion repository server. It is a source code management tool. It allows you to browse, search, monitor and analyse your code being hosted in a subversion repository.
Please consider going through the atlassian fisheye overview again available on the website.
This answer is based on your statement "As we need to move current svn repository server to Atlassian (On Demand) "