In the episode a head in the polls Nixon is pictured in the end with a huge robot body which he then goes crashing into the white house with. At which point did he decide to switch an awesome body for a headless moaning guy in a suit?
Nixon doesn't ever appear again with the huge robot body, and it isn't mentioned what happened to it.
The most likely explanation: Nixon is cheap and he just rented the body to win the election. His cheapness is supported by the fact that he bought his first robot body (i.e. Bender's body) at a pawn shop and by this dialogue from the episode:
[Scene: Outside Watergate Hotel.]
Fry: [whispering] Why would Nixon stay at the Watergate?
Leela: [whispering] They give you a discount if you've been here before.
A penny-pincher wouldn't invest more than he absolutely had to to win.