Seamless Remote Windows on Linux Client

FreeRDP (a spin-off from rdesktop) supports this in recent versions.

As far as I know, you cannot control this 20s setting.
On the other hand if what you actually want is to keep the application running on the server so the user can quickly reconnect to it and carry-on where they left off, then it is possible.

The whole process of RemoteApp disconnection is described on the Remote Desktop team blog in this article: Terminal Services RemoteApp™ Session Termination Logic.

There is a setting in the Group Policies on the server that controls how RemoteApp applications should behave when they are disconnected.
Basically, a log off is performed by default when you close a RemoteApp (after the 20s grace has elapsed), but you can change this setting to something else.

You will find the settings on the server here (for Win2008):

Local group Policies (run gpedit.msc)
  > Computer Configuration
    > Administrative Templates
      > Windows Components
        > Remote Desktop Services
          > Remote Desktop Session Host 
            > Session Time Limits
              > Set time limit for logoff of RemoteApp sessions

Note: make sure you don't override disconnect/log-off settings through the Computer Configuration or User configuration or it won't have any effect as they would have precedence.