Westwood One dropped him way back in 1992. He continued with a smaller syndicator (On The Radio Productions), for another eight years, then self-syndicated until mid-2010, when he went to online distribution only (which had been pay-for-play for four years already by then).
For the past four months, the weekly show has been repeats as a retrospective series. The last "new" show was yesterday (October 11) and was a countdown of the top 40 most requested songs during the 55 year run of the show.
Barret Hansen is a really nice guy if you know him outside of the show. We have exchanged birthday greetings via e-mail for more years than I care to remember (we're both getting old).
I should also point out that after KMET became KTWV, the live broadcast version (which was four hours long, compared to the two hour syndicated version) continued in L.A. for another ten years ... first on KLSX and then on KSCA after the former flipped from Classic Rock to Talk. The live shows ended when KSCA was sold and went Spanish language; Dr. D did a couple of specials afterwards on KSWD during its brief existence.