Are you using the TiVo or a V6? The two boxes connect to the internet (and VOD) differently so advice differs on the two.
You've both posted in the TiVo section so I'll assume here, that it's a TiVo - in which case your box has an internal dedicated cablemodem and your home broadband is immaterial and irrelevant (except that problems with one may be indicative of problems with the other).
On the front of the box, there's 3 green lights - from L>R, power, "online" that should be on permanently, and then remote input. When your VOD drops, does the middle light flash?
The last thing to check, is your live TV ok or are any channels problematic?
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