Price does affect sentiment for some grin fans, and if they are less active, the core member who in general do not much care for the price are also less motivated.
But I would not worry to much, dead is a natural part of life, through dead new life can appear.
Bitcoin will always have the first mover advantage. So unless Bitcoin wholesomely fails for some weird reason, I do not think any crypto currency project including grin is likely to beat Bitcoin in its market cap.
However, what does “beating Bitcoin mean”, what does success even mean for Grin? I can foresee a future where it is possible that grin will be more used for day to day transaction than Bitcoin, that is for sure a possibility. But even if grin would remain more obscure, for the real crypto purist and enthusiast, as long as it succeeds in being used in the real world, I would count that as “success”. Can grin succeed as “Utopian crypto project”? I for sure believe that it can succeed as such.
Personally my objective for grin is very non-abstract. One day, even if that day might still be far away, I want to go to a coffee store and buy myself a great cup of coffee using grin. Since it is Grin, I do not need to worry if spend 5 buck out of a 100000 buck output to buy a coffee, because no one but me knows. Because it is grin, I do not need to be worried that any adversary can effortlessly link my identity to that one purchase, something they can easily do when I would have used Bitcoin to buy that cup of coffee. That is my personal measure of success for grin 
.