When will hydrogen no longer be the most abundant nucleus? In a recent question, we learned why hydrogen is currently the most abundant nucleon or element in the universe.
Here I ask a follow-up: For how long will hydrogen be the most abundant nucleus?  It is most abundant now, but is slowly being consumed by nuclear fusion in the interior of stars across the universe.  Most currently existing hydrogen hasn't even made it into a star yet.  Will it ever?  If so, how long will it take?
Essentially, how many gigayears (or exayears or whatever) until hydrogen is no longer the most abundant nucleus anymore?
 A: We can only give an answer on the basis of what we currently know about cosmological parameters. If indeed these have been correctly estimated, and that the cosmological constant is constant, then the universe will continue to expand at an accelerating rate.
Given that about half the baryons in the universe currently exist outside galaxies in the "warm/hot intergalactic medium", then it seems to me quite likely that these will never form part of stars and that the increasingly rarefied universe will cease to form (many) stars in the future.
In that scenario, isolated protons would always be the most common nuclei.
One complication is that the answer may be different for that part of the universe that we can see.
Gravitationally bound systems like the Milky Way, the local group and cluster will likely not take part in the accelerating expansion. Thus the baryons within this region could continue to be processed in stars, even if they do not constitute the majority of baryons in the universe. How to estimate the timescale for this processing? A lower limit is probably the free-fall timescale of the local supercluster, which has a mass of about $10^{15}$ M$_{\odot}$ in a diameter of 33 Mpc. The free-fall timescale is $\sim (G \rho)^{-1/2} \simeq 100$ billion years. However, this time must be increased to allow that most stars formed are low-mass red dwarfs with timescales to turn hydrogen into helium of a further $10^{12}$ years. So within our local group of galaxies, I would estimate $10^{11}$ years to incorporate all the gas in our local cluster into stars and a further $10^{12}$ years for them to fuse most of the hydrogen.
