Internet Connection frequently dropping on Ethernet

My internet connection is frequently dropping on Wired Lan (Ethernet) but the wireless works fine without any problem. It's not an issue of Internet Speed as Internet works fine in Windows.

ifconfig output

$ ifconfig eth0
eth0      Link encap:Ethernet  HWaddr 44:1e:a1:db:95:d9  
          inet addr:192.168.28.127  Bcast:192.168.31.255  Mask:255.255.252.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:31254 errors:0 dropped:0 overruns:0 frame:0
          TX packets:1922 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:2729623 (2.6 MiB)  TX bytes:228959 (223.5 KiB)
          Interrupt:41 Base address:0x4000  

ethtool output

$ ethtool eth0
Settings for eth0:
    Supported ports: [ TP ]
    Supported link modes:   10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
    Supported pause frame use: No
    Supports auto-negotiation: Yes
    Advertised link modes:  10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
    Advertised pause frame use: No
    Advertised auto-negotiation: Yes
    Speed: 100Mb/s
    Duplex: Full
    Port: Twisted Pair
    PHYAD: 0
    Transceiver: internal
    Auto-negotiation: on
    MDI-X: Unknown
    Supports Wake-on: pumbg
    Wake-on: g
    Current message level: 0x00000033 (51)
                   drv probe ifdown ifup
    Link detected: yes

.

lspci output

$ lspci -kd 10ec:8136
03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI Express Fast Ethernet controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 1670
    Kernel driver in use: r8101

dmesg Output http://pastebin.com/5rWAuFkH

I tried:

• Disabling IPv6 mentioned here: https://wiki.debian.org/DebianIPv6#How_to_turn_off_IPv6 and http://forums.debian.net/viewtopic.php?f=5&t=105485
• Reinstalling the driver.
• Changing LAN Cable.

But the problem persist. Can anybody help me with this.

EDIT Full ifconfig output

$ ifconfig
eth0      Link encap:Ethernet  HWaddr 44:1e:a1:db:95:d9  
          UP BROADCAST MULTICAST  MTU:1500  Metric:1
          RX packets:153899 errors:0 dropped:0 overruns:0 frame:0
          TX packets:10625 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:16405299 (15.6 MiB)  TX bytes:3355393 (3.1 MiB)
          Interrupt:41 Base address:0x4000 

eth1      Link encap:Ethernet  HWaddr 94:39:e5:51:81:49  
          inet addr:192.168.235.102  Bcast:192.168.235.255  Mask:255.255.255.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:4213 errors:0 dropped:0 overruns:0 frame:59354
          TX packets:4797 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:2795494 (2.6 MiB)  TX bytes:712585 (695.8 KiB)
          Interrupt:16 

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          UP LOOPBACK RUNNING  MTU:65536  Metric:1
          RX packets:28 errors:0 dropped:0 overruns:0 frame:0
          TX packets:28 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:1400 (1.3 KiB)  TX bytes:1400 (1.3 KiB)

vmnet1    Link encap:Ethernet  HWaddr 00:50:56:c0:00:01  
          inet addr:172.16.222.1  Bcast:172.16.222.255  Mask:255.255.255.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:10 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)

vmnet8    Link encap:Ethernet  HWaddr 00:50:56:c0:00:08  
          inet addr:172.16.31.1  Bcast:172.16.31.255  Mask:255.255.255.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:10 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)

EDIT2

VmWare Network Configruations

Note: These were the default configurations, I didn't changed them. I just added VM.

vmnet0

vmnet1

vmnet8

My suspicions are raised by the follwoing lines in your dmesg output:

[  112.906696] bridge-eth0: disabling the bridge on dev down
[  112.906765] bridge-eth0: down
[  112.906779] bridge-eth0: detached
[  113.106574] userif-3: sent link down event.
[  113.106584] userif-3: sent link up event.
[  114.910231] r8101: eth0: link up
[  114.910591] /dev/vmnet: open called by PID 3068 (vmnet-bridge)
[  114.910628] /dev/vmnet: hub 0 does not exist, allocating memory.
[  114.910697] /dev/vmnet: port on hub 0 successfully opened
[  114.910724] bridge-eth0: up
[  114.910759] bridge-eth0: attached

I would try the following: it is just a try, if it does not produce the desired results, just turn the pc off and on again, and you have the same situation as before the trial.

1. Block the VM, kill VMWare completely.
2. Block netwwork manager (sudo service network-manager stop);
3. Connect manually (sudo dhclient eth0).
4. Try navigating for some time, and see whether the same problem resurfaces.

Let us know.