The BEA has quarterly national accounts back to 1947. During that time (62 years), nominal GDP NEVER fell while real GDP grew, even for a single quarter.
The BEA has annual national accounts back to 1929. During that time, nominal GDP NEVER fell while real GDP grew. Judging from the annual rates, it's possible that it happened for a quarter during 1933 or 1938.
[The BEA has monthly consumption back to 1959, during that time (599 months) nominal consumption fell while real consumption grew only two or three times: Nov 2008, Sep 2006, and maybe Dec 2001 (real consumption was essentially constant here)].
But it may have happened in 2008 Q4! Even I am confident that nominal GDP fell in Q4. But I have noted the significant (but still less than one half) probability real GDP grows in Q4.
Milton Friedman mentioned that it happened several times in history prior to the Great Depression -- does anyone have that reference? I suspect it is in his AEA presidential address, but maybe in the Monetary History.
[update (via Tino): p. 97 of the Monetary History says "From 1891 to 1896 net national product in current prices fell at an average rate of roughly 1 per cent per year, and in constant prices rose at a rate of roughly 2 per cent per year." Chart 16 seems to show some real income growth 1927-27, but a money income decline.]