What is “rating oblivion” of TV shows?

My interpretation is that it is a jargon-y way of saying 'ratings so low there is no longer any hope of raising them'; 'oblivion rate', in this context, would not make sense (hence why it was not used), as that would imply 'oblivion' is either some measure of speed or a metric of ratings (depending on your interpretation of 'rate').

Oblivion is a "state of being disregarded or forgotten", and ratings oblivion is a non-idiomatic term for being quite low in the ratings.

Ratings in this case refers to estimates of viewership, such as Nielsen Ratings:

When TV viewers or entertainment professionals in the United States mention "ratings" they are generally referring to Nielsen Ratings, a system developed by the New York City-based firm Nielsen Media Research to determine which shows television viewers watch at what times. Other ratings systems include those developed by Arbitron for radio programming and the Q Score for general markets.

Olbermann was hired by Current TV in January, 2011; while some articles refer to him failing to save Current TV from "the throes of ratings oblivion", others emphasize breach-of-contract as the reason for him being fired.

Oblivion derives from Latin oblīviōn-em forgetfulness, state of being forgotten.

Ratings in this context means television viewership ratings (I'm not keen on the word viewership, but I just cut & pasted from Wikipedia).

As zandomatter says, the combination ratings oblivion is really just "industry jargon". But since the media industry talks about itself a lot, it's well-known to most native speakers.

If your tv show is at the bottom of the ratings league, by implication the audience have already forgotten it, so you can forget about striking a lucrative deal with advertisers/sponsors, or planning a new series.