Will new stars stop forming at some point of time?
Cosmic GDP has already crashed, as Peak Star was ~11 billion years ago.


According to Sobral et al's prediction, the future star production by mass will give only 5% of the stars in the universe today, "even if we wait forever." More theoretical predictions, such as this one, suggest that nebulae will run out of hydrogen on the order of $10^{13}$ years, while star formation will occasionally happen due to collision of brown dwarfs until somewhere on the order of $10^{14}$ years.

Of course, hydrogen itself may have a finite lifetime. The half-life of a proton is experimentally known to be longer than $10^{34}$ years, but it may still be quite finite.