Low upload speed (CentOS 6)

I've been having an issue with my servers upload speed slowing down for the last week. When it first occurred restarting the network service would resolve the slow speeds. The speed would then be okay for anywhere from 24 to about 72 hours and then slow down to a crawl again. Today when I rebooted the network service the server hung and I had to manually reboot the server.

I am running CentOS 6.5 with the latest OpenVZ kernel as the server is used to host vps servers. If I need to provide any other information please let me know. I have other servers with essentially the same configuration with this company and this is the only server experiencing this issue. The company guarantees 100MB/s. When things slow down I get about 20 kb/s when trying to download a test file off the server.

ethtool:

Settings for eth0:
        Supported ports: [ TP ]
        Supported link modes:   10baseT/Half 10baseT/Full
                                100baseT/Half 100baseT/Full
                                1000baseT/Full
        Supported pause frame use: No
        Supports auto-negotiation: Yes
        Advertised link modes:  10baseT/Half 10baseT/Full
                                100baseT/Half 100baseT/Full
                                1000baseT/Full
        Advertised pause frame use: No
        Advertised auto-negotiation: Yes
        Speed: 100Mb/s
        Duplex: Full
        Port: Twisted Pair
        PHYAD: 2
        Transceiver: internal
        Auto-negotiation: on
        MDI-X: on
        Supports Wake-on: pumbg
        Wake-on: g
        Current message level: 0x00000007 (7)
                               drv probe link
        Link detected: yes

dmesg |grep e1000e

    [    2.204393] e1000e: Intel(R) PRO/1000 Network Driver - 2.3.2-k
[    2.204395] e1000e: Copyright(c) 1999 - 2013 Intel Corporation.
[    2.204417] e1000e 0000:00:19.0: PCI INT A -> GSI 20 (level, low) -> IRQ 20
[    2.204422] e1000e 0000:00:19.0: setting latency timer to 64
[    2.204503] e1000e 0000:00:19.0: Interrupt Throttling Rate (ints/sec) set to dynamic conservative mode
[    2.204531] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[    2.404296] e1000e 0000:00:19.0: eth0: registered PHC clock
[    2.404299] e1000e 0000:00:19.0: eth0: (PCI Express:2.5GT/s:Width x1) f8:b1:56:b8:96:fe
[    2.404300] e1000e 0000:00:19.0: eth0: Intel(R) PRO/1000 Network Connection
[    2.404327] e1000e 0000:00:19.0: eth0: MAC: 10, PHY: 11, PBA No: 5041FF-0FF
[    3.619389] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[    3.720105] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[    5.249001] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[    5.249010] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  299.993906] e1000e: eth0 NIC Link is Down
[  301.777634] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  301.777639] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  301.789655] e1000e: eth0 NIC Link is Down
[  303.640797] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  303.640802] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  312.563531] e1000e: eth0 NIC Link is Down
[  314.248255] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  314.248260] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  368.737532] e1000e: eth0 NIC Link is Down
[  370.470445] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  370.470449] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  370.871902] e1000e: eth0 NIC Link is Down
[  372.566629] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  372.566633] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[  372.650533] e1000e: eth0 NIC Link is Down
[  374.402633] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[  374.402638] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91265.671501] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[91265.772193] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[91269.900310] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91269.900320] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91298.315872] e1000e: eth0 NIC Link is Down
[91300.049356] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91300.049373] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91312.163795] e1000e: eth0 NIC Link is Down
[91313.835394] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91313.835397] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91315.412871] e1000e: eth0 NIC Link is Down
[91317.218629] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91317.218641] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91449.457109] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[91449.557589] e1000e 0000:00:19.0: irq 69 for MSI/MSI-X
[91451.105209] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91451.105213] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91451.191593] e1000e: eth0 NIC Link is Down
[91452.905469] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91452.905475] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO
[91454.344927] e1000e: eth0 NIC Link is Down
[91456.040457] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: None
[91456.040465] e1000e 0000:00:19.0: eth0: 10/100 speed: disabling TSO

netstat -i

Kernel Interface table
Iface       MTU Met    RX-OK RX-ERR RX-DRP RX-OVR    TX-OK TX-ERR TX-DRP TX-OVR Flg
eth0       1500   0 11192854     21      0      0 10035615      0      0      0 BMRU
lo        16436   0        1      0      0      0        1      0      0      0 LRU
venet0     1500   0  9972546      0      0      0 10747306      0      1      0 BOPRU

ifconfig eth0

eth0      Link encap:Ethernet  HWaddr F8:B1:56:B8:96:FE
          inet addr:xxxxxxxxxx  Bcast:xxxxxxxxxx  Mask:xxxxxxxxxx
          inet6 addr: xxxxxxxxxx/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:11200159 errors:21 dropped:0 overruns:0 frame:11
          TX packets:10043059 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:6744462142 (6.2 GiB)  TX bytes:4788632826 (4.4 GiB)
          Interrupt:20 Memory:fbf00000-fbf20000

You don't provide much context around the dmesg timing, but if this is off of a fresh boot that immediately started exhibiting the problem, then your issue is that the switch port is flapping, which could be caused by just about anything (your driver, your hardware, the cable, switch's hardware, or the switch's configuration). Given that you said this is being hosted by a "company", the support division of any hosting company worth even a fraction of their salt should take this issue at least as far as eliminating everything other than your driver from consideration as the culprit (e.g. by plugging in and testing with an alternate piece of hardware). A managed hosting company (like BlackMesh or Rackspace) would take care of the whole issue from end-to-end.