I have this exact same issue as well. Videos will begin to download at full speed, only to slow down and stop within 10 seconds of starting. This has been a problem for well over a year now, and I have never seen it happen anywhere else.

From a residential ISP (Bellsouth DSL) - 

 

C:\dev>tracert ecn.channel9.msdn.com

Tracing route to mschannel9.vo.msecnd.net [65.55.87.90]
over a maximum of 30 hops:

1 1 ms <1 ms <1 ms 192.168.1.1
2 6 ms 5 ms 5 ms adsl-74-161-129-1.mia.bellsouth.net [74.161.129.1]
3 5 ms 5 ms 6 ms 205.152.108.1
4 5 ms 5 ms 5 ms her00mia-ge-6-3.bellsouth.net [205.152.145.161]
5 26 ms 6 ms 6 ms 12.81.8.94
6 5 ms 5 ms 5 ms 12.81.8.67
7 11 ms 10 ms 10 ms 74.175.192.170
8 41 ms 43 ms 44 ms cr81.fldfl.ip.att.net [12.122.106.94]
9 43 ms 43 ms 43 ms cr2.ormfl.ip.att.net [12.122.1.45]
10 44 ms 43 ms 42 ms cr1.ormfl.ip.att.net [12.122.5.185]
11 45 ms 42 ms 42 ms cr2.hs1tx.ip.att.net [12.122.1.5]
12 43 ms 43 ms 43 ms cr1.dlstx.ip.att.net [12.122.28.157]
13 44 ms 43 ms 43 ms cr2.dlstx.ip.att.net [12.122.1.210]
14 40 ms 41 ms 43 ms cr81.ftwtx.ip.att.net [12.122.100.69]
15 38 ms 39 ms 38 ms gar5.auttx.ip.att.net [12.122.100.73]
16 40 ms 40 ms 40 ms 12.248.87.6
17 40 ms 40 ms 40 ms 204.152.140.17
18 49 ms 49 ms 48 ms xe-8-2-0-0.sn1-96cb-1a.ntwk.msn.net [207.46.46.179]
19 46 ms 46 ms 47 ms 10gigabitethernet5-1.sn1-xmx-edgcom-1b.ntwk.msn.net [207.46.33.110]
20 48 ms 48 ms 50 ms cds85.sat9.msecn.net [65.55.87.90]