I have had this problem since I first got BT Vision (about 7-8 months ago). The problem has reduced in severity (i.e. it started out that I could only watch a few seconds of VoD before it failed, now I can watch a whole 10-15 minutes... albeit with glitches) but the problem is still present.
I have spent hours (literally and on multiple occaisions) on the phone with BT - calls that I was then charged for. Last time round, the call with BT concluded with the BT guys saying "Yes, the problem seems to be a known issue here" and that someone would be in touch when it was fixed. A few weeks later they left a message on my answerphone sayiong it was all sorted - the problem is unchanged and I am fed up with being repeatedly charged for BT's inability to solve the problem.
For the avoidance of doubt, speed is not an issue and BT have repeatedly said that my connection is suitable for BT Vision.
Looking at the BT Beta forums, the problem is not that unusual - but I think that it might be hard to fix, specifically I suspect there might not be a silver bullet solution. Certainly I have not yet seen anything where there is a concensus the "This fixes the problem".
Given the repeated interruptions to BT's e-mail service, the recent 'upgrade' of said e-mail service and the woes of BT Vision (not to mention the poor content), I am now patiently waiting for my contract to expire when I will cheerfully, gleefully sack BT as my provider. Until then, all I can do is hold myself up as a warning for others - make the wrong choices and you could end up like me!
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Life does not cease to be funny when someone dies, any more than it becomes happy when someone laughs.