How to avoid F5 BIGIP LTM close the connections?

Just one point here, you should create a new TCP profile with a parent of the main TCP profile and just make the changes required to your new profile. If you make major changes to the main TCP profile this will affect a number of virtual servers. Obviously, leaving connections open for a long period has an impact on the f5 so should be limited only to virtual servers where it is required, and use the shortest possible timeout. eg 1 hour rather than indefinite. There are a number of settings available, these should be considered for their benefits Look Here