RemoteApp 2012 – App is flickering

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.

It sounds like your RemoteApp's .rdp file (or RDweb "source name") may refer to a hostname that can be resolved only on the LAN, or perhaps it refers to an RFC 1918 IP address.

Using an .rdp file:

1. Open the RemoteApp's .rdp file in Notepad.
2. Verify that the hostname in the .rdp file is resolvable outside the LAN. For example, at a command prompt, you could type "nslookup hostname.domain 8.8.8.8" to see whether it can be resolved by Google Public DNS.
3. If the hostname in the RDP file cannot be resolved from the public internet, or if it resolves to an RFC 1918 IP address, use Notepad to substitute the server's FQDN (or public IP address).
4. In Notepad, choose File -> Save.
5. Transfer the modified .rdp file to the remote computer and then retry opening the RemoteApp by double-clicking on the .rdp file.

Using RD Web Access:

1. Logging in as "administrator" on the https://terminalserver/rdweb configuration page.
2. Make a similar configuration check/change to the RemoteApp Source Name. Again, it must be a fully qualified domain name or routable IP address; if it is a NetBIOS name, it won't work outside the LAN.

[Disclaimers: (1) I have never personally deployed or used RD Web Access. (2) I have never served a RemoteApp to a computer outside my LAN without requiring a VPN connection. The potential security benefits of requiring a VPN connection are beyond the scope of this question, but, in my opinion, they should be considered carefully before allowing any kind of RDP access from outside a trusted local area network.]