RDC ,Terminal server exceeded maximum number

[zillah]

I have got two PCs (Desktop and Laptop) 2003 server, I have got these users on Desktop :
username
pfan-->password : pfan-->Member of Group: Remote Desktop Users
nshoe-->password: nshoe-->Member of Group: Remote Desktop Users
When I tried to login from laptop to Desktop as username:Administrator and its associated password,,there is no problem
When I tried to login from laptop to Desktop as username : pfan (there is no other concurrent (simultenous) remote desktop connection) and its associated password,,I am receiving this error connection:

Terminal server has exceeded maximum number of allowed connection".

And when I tried to login from laptop to Desktop as username:nshoe (there is no other concurrent (simultenous) remote desktop connection) and its associated password,,I am receiving the same error above.
1- Why Am I recieving this error message ?
2- How many concurrent Remote Desktop Connection for different(obvious for the same user from different PCs, I can not have) users can I have ?

[twwabw]

Are you running 2003 server on each of these? Or which ones?

[zillah]

Are you running 2003 server on each of these? Or which ones?
Yes I am running win2003 on both of them.

[twwabw]

Server2003 supports 2 simultaneous connections, for the purpose of administration. When you end a session, are you logging off the session, or simply closing (X'ing out) the session? This is leaves you still connected. Does the condition still occur after a fresh reboot of both?

[zillah]

When you end a session, are you logging off the session, or simply closing (X'ing out) the session? This is leaves you still connected.
Yes this was the problem. I have to right click then "Logoff" to solve the problem

Does the condition still occur after a fresh reboot of both?
No.