It seems that watching time at a booth of an NHK library is limited to one or two hours per application.
If you have a chance to visit an NHK program library in Japan but its booth is crowded, maybe you cannot watch at once the whole of a Kouhaku Utagassen program of a specific year.
In the past until 1970s or so, recording media such as film and videotape were so precious that Japanese broadcasters did not preserve all major programs; this applied even to big annual programs like the Kouhaku.
And, before recorded programs are reused, some need restoration, and some require consent of people appearing there and/or holders of intellectual property rights such as songwriters.
As for now, most of NHK Kouhaku Utagassen programs from 1954 to 2011 are kept in NHK Archives and about 1/4 of them are available in a program library, but some have missing portion and some are preserved only in highlight or digest edition.
Search result in Japanese
(Conditions = title including "Kouhaku Utagassen" in kanji characters, available at a program library):
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http://cgi2.nhk.or.jp/chronicle/list.cgi?q=%E7%B4%85%E7%99%BD%E6%AD%8C...1965/12/31 (the 16th): 2 portions;
1968/12/31 (the 19th): (re-aired on 2002/12/19 at BS-2);
1969/12/31 (the 20th): 3 portions;
1971/12/31 (the 22nd): 2 portions;
1972/12/31 (the 23rd): 2 portions;
1974/12/31 (the 25th): 2 portions;
1976/12/31 (the 27th): 2 portions;
1977/12/31 (the 28th): 3 portions;
1978/12/31 (the 29th): 2 portions;
1979/12/31 (the 30th): 3 portions;
1980/12/31 (the 31st): 2 portions;
1982/12/31 (the 33rd): 2 portions;
1983/12/31 (the 34th): 3 portions;
1984/12/31 (the 35th): 2 portions;
1985/12/31 (the 36th): 2 portions;
1988/12/31 (the 39th): 2 portions.
NHK Archives: Brochure:
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http://www.nhk.or.jp/archives/kawaguchi/about/Archives_6p_E.pdf
