Nothing is perfect, everything has friction---except in quantum physics, where macroscopic superconductors allow for dissipationless currents. It's an astounding theoretical prediction, and so it is interesting to know the best experimental lower bound on the lifetimes of supercurrents.
Surprisingly, the best (and one of the only) paper(s) which I could find on this topic is a Physical Review Letter from 1963 [J. File and R. G. Mills, PRL 10, 93 (1963)]. They measured a supercurrent for 37 days and from their measurements on the decay of the current, they could confidently extrapolate the lifetime to $\gtrapprox 10^5$ years.
Has there been any experimental work since then that breaks this record?
Interestingly, this book (available on google books) claims that Gallop ran a current for nearly three years to determine its lifetime! That is a whopping increase over File's and Mills' 37 days. Alas, the author does not give a reference (disclaimer: it could be that a reference is hiding in a part of the book that I cannot access).