If pressing ESC at the first time of dreaming the Eldritch, the dream will stop and the research won't unlock, and the player cannot dream the Eldritch again.

Hmmm, did you Dream of Void again? You first need to have Dreamt of Void before being able to get the Eldritch Dream (although it's my fault for not having made it clearer in Al Azif). The Dream of Void is expended each time one makes a Dream that utilizes it (such as the Eldritch one) and must be performed again.
If that isn't the problem I'll look into it.

Ah, I didn't realize that Dream of Void is a kind of consumables before - I thought it changed the dream forever.
And yes, with the help of Void Dream, the Eldritch is available again.
So the issue can be closed. (Maybe it is a good idea to make the method much clear in Al Azif)
By the way, would you please tell me whether the "lengthen" effect of Void Dream works for any other Dreams or is only useful to the Eldritch Dream?

It's not really a "lengthen" effect as much as an "empower" one. Right now, it's going to increase the effectiveness of Effect Dreams (i.e. Power, Stillness and Change) by making the effects more powerful and/or last longer.
It can also work with the Dream of Darkness: if you're under the influence of Void, then as well as the Voided biome location it will also try to tell you the location of a Hamlet, provided at least one has been generated in the world.

I'm not going to close the issue yet so that I remind myself to make the description clearer in Al Azif.

Ok, I got it. Thanks!