I would be appriciated if someone could answer my question.....

Well this is something I've never heard of but I have some ideas. Realize they could be off the mark but you can check them out. Assumptions: you are playing MP with your own server and two or more 'puters on a LAN. If the assumptions are wrong please provide more information.

Every time a player on a server logs off, undocks, docks and jumps a hole or gate, the server saves the character in a FL saved game file. That of course includes the current reputations. So you should check the FL MP saved game file by using something to decrypt the file (I use the FL Save Editor). Look for all the lines starting with house, there is an example below:

house = 0.007, rh_n_grp

If the 0.007 is all 0's then there is where you are getting all your neutrality from since 1 is very friendly, -1 is very unfriendly and 0 is neutral. If there are nothing but zero's you have some significant problem with either your server (maybe not) or client installation. Maybe a mod is resetting these.

It's also possible it's some initialization error and defaults reps to 0. Check FLspew.txt on the client and the CONSOLE messages on the server. The closest thing to message logs for flserver is fl-server-errors.log on the root directory of the drive flserver is installed in and FLServer_cheaters.log in the MP directory deep under My Documents which just shows all those flserver itself banned.

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Earendil
SysAdmin of Boston Freelancer server
Server community website & forum: EarendilsPlace.net (server rules)

Sorry for the poor description. Made an assumption that people knew what I was talking, but then realized that better desription would have lead to an answer.
With said, then let's go to the topic....

Yes, there was talking about LAN-gaming in it's entirety. So from what you're saying, Earendil, the reputation shouldn't neutralize, after the clients has logged off. Well, this does occur, i.e. the reputation are retained after client log-off. But what if the server was shut down also, should the reputation still be retain. If not, then may be a system error? And how do I solve it?
Because that may be the problem.

Well as mentioned all information about each and every character on a server is kept in it's own FL saved game file. It has an extension of .fl and is encrypted. If it is unecrypted you would see lines of data as I put above.

This at least would tell you if flserver is messed up or the file is messed up. You could even edit the file and see if this propogates through to your next log on!

You could also check the initialworlds.ini file under the DATA directory of the server. After decryption, there are lines like:

rep = 0.65, rh_n_grp

which (I believe) direct the new character's reputations when they are created. As you can see when your character is created it will be relatively friendly with the Rheinland Navy. If the files are changing after you log off/log back on then there is another problem and thus looking at the initialworlds.ini file is not needed.

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Earendil
SysAdmin of Boston Freelancer server
Server community website & forum: EarendilsPlace.net (server rules)

Interesting is this referring to the neutral condition i see in multiplayer? I have been playing multiplayer and the map patrol path only shows neutral path although i have friendlies and enemies.