Huawei K3565 Rev 2 (12d1:140c): Randomly disconnects from mobile broadband network and behaves as if USB modem physically disconnected

I connect to a mobile broadband network through a Huawei USB 3G modem.
I stay connected all the time.

Every once in a while, with almost systematic periodicity (like every 20-30 minutes), without any apparent reason, whether or not I am using the network or not, the nonnection suddenly goes down, and:
- the indicator shows I'm disconnected, the
- the mobile broadband networks (I have two of them configured, though I only use one now) disappear from the list in nm-applet
- The option "Enable Mobile Broadband" at the bottom of the nm-applet menu DISAPPEARS (not that it gets unchecked, it _disappears_ completely)

In order to reconnect I have to unplug and replug the usb modem, wait a few seconds for it to be initialized or whatever, and then reconnect via the nm-applet (when the nm-applet doesn't become unresponsive because of another old known bug).

All the symptoms are EXACTLY as if someone had suddenly unplogged the modem physically, so this may as well be a usb problem.

I have no idea what logs I should look for and attach.

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: network-manager 0.9.4.0-0ubuntu4.2
ProcVersionSignature: Ubuntu 3.2.0-33.52-generic 3.2.31
Uname: Linux 3.2.0-33-generic i686
NonfreeKernelModules: nvidia
ApportVersion: 2.0.1-0ubuntu14
Architecture: i386
Date: Fri Oct 26 20:10:24 2012
IfupdownConfig:
 auto lo
 iface lo inet loopback
InstallationMedia: Ubuntu 10.04 LTS "Lucid Lynx" - Release i386 (20100429)
IpRoute:
 default via 10.64.64.64 dev ppp0 proto static
 10.64.64.64 dev ppp0 proto kernel scope link src 77.210.172.228
 169.254.0.0/16 dev ppp0 scope link metric 1000
NetworkManager.state:
 [main]
 NetworkingEnabled=true
 WirelessEnabled=true
 WWANEnabled=true
ProcEnviron:
 TERM=xterm
 PATH=(custom, user)
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: network-manager
UpgradeStatus: Upgraded to precise on 2012-05-17 (162 days ago)
mtime.conffile..etc.NetworkManager.NetworkManager.conf: 2012-08-30T13:38:55.126319
nmcli-dev:
 DEVICE TYPE STATE DBUS-PATH
 ttyUSB0 gsm connected /org/freedesktop/NetworkManager/Devices/19
 wlan0 802-11-wireless disconnected /org/freedesktop/NetworkManager/Devices/1
 eth0 802-3-ethernet unavailable /org/freedesktop/NetworkManager/Devices/0
nmcli-nm:
 RUNNING VERSION STATE NET-ENABLED WIFI-HARDWARE WIFI WWAN-HARDWARE WWAN
 running 0.9.4.0 connected enabled enabled enabled enabled enabled
---
ApportVersion: 2.0.1-0ubuntu14
Architecture: i386
DistroRelease: Ubuntu 12.04
InstallationMedia: Ubuntu 10.04 LTS "Lucid Lynx" - Release i386 (20100429)
NonfreeKernelModules: nvidia
Package: network-manager
PackageArchitecture: i386
ProcEnviron:
 TERM=xterm
 PATH=(custom, user)
 LANG=en_US.UTF-8
 SHELL=/bin/bash
ProcVersionSignature: Ubuntu 3.2.0-33.52-generic 3.2.31
Tags: precise running-unity
Uname: Linux 3.2.0-33-generic i686
UpgradeStatus: Upgraded to precise on 2012-05-17 (163 days ago)
UserGroups: adm admin audio cdrom dialout lpadmin netdev plugdev sambashare vboxusers video
---
AlsaVersion: Advanced Linux Sound Architecture Driver Version 1.0.24.
ApportVersion: 2.0.1-0ubuntu14
Architecture: i386
AudioDevicesInUse:
 USER PID ACCESS COMMAND
 /dev/snd/controlC0: teo 2582 F.... pulseaudio
Card0.Amixer.info:
 Card hw:0 'Intel'/'HDA Intel at 0xfebf8000 irq 49'
   Mixer name : 'Realtek ALC660-VD'
   Components : 'HDA:10ec0660,10430000,00100001 HDA:10573055,10431316,00100700'
   Controls : 28
   Simple ctrls : 16
DistroRelease: Ubuntu 12.04
HibernationDevice: RESUME=UUID=b1b3e5fe-38e2-44c9-9e48-4564cd9f4d66
InstallationMedia: Ubuntu 10.04 LTS "Lucid Lynx" - Release i386 (20100429)
MachineType: ASUSTeK Computer Inc. M51Sn
NonfreeKernelModules: nvidia
Package: network-manager
PackageArchitecture: i386
ProcEnviron:
 TERM=xterm
 PATH=(custom, user)
 LANG=en_US.UTF-8
 SHELL=/bin/bash
ProcFB: 0 VESA VGA
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-3.2.0-33-generic root=UUID=173acbf5-26a0-49e3-8d2b-f1c142582cbf ro quiet splash vt.handoff=7
ProcVersionSignature: Ubuntu 3.2.0-33.52-generic 3.2.31
RelatedPackageVersions:
 linux-restricted-modules-3.2.0-33-generic N/A
 linux-backports-modules-3.2.0-33-generic N/A
 linux-firmware 1.79.1
StagingDrivers: zram
Tags: precise running-unity staging precise running-unity
Uname: Linux 3.2.0-33-generic i686
UpgradeStatus: Upgraded to precise on 2012-05-17 (163 days ago)
UserAsoundrc:
 pcm.!default { type pulse }
 ctl.!default { type pulse }
 pcm.pulse { type pulse }
 ctl.pulse { type pulse }
UserGroups: adm admin audio cdrom dialout lpadmin netdev plugdev sambashare vboxusers video
dmi.bios.date: 12/24/2007
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: 303
dmi.board.asset.tag: ATN12345678901234567
dmi.board.name: M51Sn
dmi.board.vendor: ASUSTeK Computer Inc.
dmi.board.version: 1.0
dmi.chassis.asset.tag: ATN12345678901234567
dmi.chassis.type: 10
dmi.chassis.vendor: ASUSTeK Computer Inc.
dmi.chassis.version: 1.0
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvr303:bd12/24/2007:svnASUSTeKComputerInc.:pnM51Sn:pvr1.0:rvnASUSTeKComputerInc.:rnM51Sn:rvr1.0:cvnASUSTeKComputerInc.:ct10:cvr1.0:
dmi.product.name: M51Sn
dmi.product.version: 1.0
dmi.sys.vendor: ASUSTeK Computer Inc.