I don't know about TiVos in general, but ...
When my DirecTV TiVo remote fell about 2 inches onto the floor and somehow stopped working completely, I called up DirecTV to tell them my sob story. This was around 4 p.m. They say they can get me a new remote, and it should take about 3 business days. They also tell me there really aren't any authorized dealers in my area. So I'm not thrilled about having to control the box with the buttons on the box itself for a couple of days, but so be it.
Next morning, I'm harshly awaken from a dirty Scarlett Johanssen dream by the doorbell at 9 a.m. It's a dude from the post office, asking me to sign for a package. Obviously, I wouldn't be telling you this if it wasn't the remote. Not only that, but it was a new universal one that lets me control basically everything I have with one remote. And they never even charged me for it.
Love me some DirecTV after that.