White, who had been slurring her speech for 30 minutes before being replaced by fellow DJ Denholm Siergertz, told listeners she was letting them pick the songs because she was having a "P-A-R-T-Y."
When one listener texted White to say she sounded drunk, the 16-year veteran responded, "I'm not drunk. I've had a couple of drinks, but I'm not drunk."
Her BBC bosses apparently felt otherwise, because they decided to cut her last day short by two hours and 30 minutes.
A BBC spokesman later said White was "unable to continue as she was under par."
It was unclear if White faced additional disciplinary action for her behavior.
"Paula has done so much for the community that I think it would be unfair if she was to be remembered for something like this," said her friend, Sentinel columnist Fred Hughes.