Firstly, Netflix is an online app and relies on an internet connection - the TiVo has this built-in but if there's a problem with it, Netflix will be affected (as will all your VOD, iPlayer, and every other app). On the front-left of the box there's a series of green lights - second from left has a heart symbol next to it and indicates your "online" connection status. This should be on solidly, but if it flashes that's a fault.
Indeed, if the box is rebooting or losing the online light during any app session, that's a fault and your box should get replaced like-for-like no issues.
Second, the TiVo box while being perfectly serviceable, is quite old by current standards and has long been superceded by the V6 box. If you have VM broadband (it's a requirement) and have had your current package for a while, you could do a lot worse than investigate a newer (potentially cheaper) bundle and get a swapout to a V6 as part of the bargain.
The V6 is much newer, much quicker, and has 6 recording tuners rather than TiVo's 3. And as an example, iPlayer loads in about 10-15 seconds on the V6.
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