Keeping launcher open too long causes 'Invalid Session' errors

When keeping the launcher open for several days, eventually joining servers fails with the error 'Invalid Session'.

The client seems logged in with a valid Session ID, however this is not true. When I restart the launcher, the Session ID changes. When I repeatedly close and re-launch the launcher, the Session ID stays at this new value.

NB: I downloaded the newest Minecraft Launcher EXE, which is 1.6.5, however I cannot select this version in the Affected Version/s field.

Client log:

[18:20:32] [Client thread/INFO]: Setting user: youtakun
[18:20:32] [Client thread/INFO]: (Session ID is token:d6f1f5e7e14a401986faeab8c70feffe:43f517c0028a437bb1e2daf140c80ff1)
[18:20:33] [Client thread/INFO]: LWJGL Version: 2.9.4
[18:20:33] [Client thread/INFO]: Reloading ResourceManager: Default, faithful32pack.zip
[18:20:34] [Sound Library Loader/INFO]: Starting up SoundSystem...
[18:20:34] [Thread-6/INFO]: Initializing LWJGL OpenAL
[18:20:34] [Thread-6/INFO]: (The LWJGL binding of OpenAL.  For more information, see http://www.lwjgl.org)
[18:20:34] [Thread-6/INFO]: OpenAL initialized.
[18:20:34] [Sound Library Loader/INFO]: Sound engine started
[18:20:35] [Client thread/INFO]: Created: 1024x1024 textures-atlas
[18:20:37] [Client thread/INFO]: Connecting to minecraftsig.serveminecraft.net, 25565
[18:20:40] [Client thread/INFO]: Stopping!
[18:20:40] [Client thread/INFO]: SoundSystem shutting down...
[18:20:40] [Client thread/WARN]: Author: Paul Lamb, www.paulscode.com
Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release

Server log:

[18:20:27] [Server thread/INFO]: com.mojang.authlib.GameProfile@1356c9dd[id=<null>,name=youtakun,properties={},legacy=false] (/217.122.174.9:4387) lost connection: Disconnected