Windows XP Professional only allows 10 simultaneous connections to shares and printer spoolers. The eleventh user gets a System error #71 message. The unused connections get freed after 30 minutes which is a bit late since often you just need a few files or to print some pages but this blocks the connection for 30 minutes.
To make things better, you can issue the command
net config server /autodisconnect:3which sets the limit to 3 minutes. You can even set this to 0 to free a slot almost instantly.
This value can also be changed in the registry. The key is HKLM\System\CurrentControlSet\Services\LanmanServer\Parameters.
More information can be found at KB138365.
The really evil can fly to Google Cache and get a disassembled part of the srvsvc.dll with the needed changes to disable the limit. (Only works for XP-SP2!)
The last resort is to upgrade to Windows Server. Another thought might be to connect to the shares from a Linux box and let the clients connect to this Linux machine.