There is no reference anywhere nor do I remember ABC ever re-airing the anthology series. The only other television broadcast I am aware of was in 2009. On August 26th, September 2nd and 9th VH-1 and VH-1 Classic re-aired the three-part series during the buildup to the remastered Beatles catalog.
I got it wrong about which part of the year it was but it did re-air on ABC in 1996 on August 31, September 5 and 7.
It's mentioned in a paragraph 8(?) in the Beatlenews Roundup in Beatlesfan Vol. 7 No. 5 (July-August 1996).
I stand corrected. Kudos for finding the source! Now we know of 3 US broadcasts. 1995, 1996 and 2009. It'd be great if someone had a copy of the 2009 VH-1 broadcast. That being only 15 years ago the tapes would be a lot fresher.
It would be something to see, wouldnt it? I mean it would be out there somewhere......maybe