I know that many others have addressed this before me, but I'd say that the main reasons why Prescott has kept popping up since the election are these: Prescott is now a loose cannon within the Labour Party. He has no formal role within either UK politics or the Labour party any more (he's no longer on the Labour National Executive Committee, and isn't even a Privy Councillor any longer). He takes the Labour whip in the Lords, but that's something of a minor matter in the grander scheme of things.
He would love to be involved in something important (e.g. he tried and failed to be the Police Commissioner for Humberside, and I have little doubt that he'll run for elected Mayor of Hull if the post ever gets created). Therefore he's very keen to keep his public profile high. And there's nobody within the Labour Party who has the power, authority or ability to shut him up.
And from the media's side, having John Prescott as a guest in the wake of the election is a mouth-watering proposition. Why? 1) You're assured of getting juicy quotes from him - he's usually outspoken, often controversial, and occasionally sensational; 2) he's undoubtedly being seen as a person who might provide a perspective on Labour's poor performance in the election (and on the election in general) from an interesting and different position - in particular, he will have words to say on why he think Labour got it so badly wrong in 2015, and where the party should go now; 3) even though it's often overlooked, he was a very big beast within the Labour Party - and, by extension, within the UK Government - between 1997 and 2010: he held important offices of state as well as the DPMship, and was an important component of the New Labour project. He also is extremely recognisable and identifiable by most of the population of the UK, and the media know that many more people will want to hear what Prescott has to say than (for example) Jack Straw or Alistair Darling.
And that, in a (very large!) nutshell, is why Prescott probably keeps popping up in the media at the moment.