I understand your need to keep logged on.
I have seen it done in other systems/environments e.g. main frame. It is possible to do it through ABAP code which would be running in the background when you logon. However one needs to consider the pros and cons of such processes/procedures. It certainly gives you the advantage of not being logged off. However this poses a security risk, as some one else may be able to use your logon and cause problems not only for yourself but to the organisation you are working for.
The reason that a person is logged off if he/she has not been actively using it for a set time limit is to avoid the risk to security and integrity of data. This is a common and normal standard in a production environment using Best Practices. Before you plan to avoid the logging off, you need to see if your employer sees this as against its standards.