Dear Fellow Enthusiast- Re: the "why": Because, as per caution by his "time travelling" professor, you can "not" have any indicators or triggers that will recall the present, and that's what removed him from 1912.
Not sure about the 2nd. part of your query re: what happens in those days? I presume you mean the days subsequent to his return to present? Well, after failing to get back to the past, he seemed to enter a catatonic state and wasted away untill discovered when they entered his room... Questions??

My Best & continue to enjoy the "escape"! Lar

I know exactly what you mean Lizzette35. I have been scouring the internet to see what others theorize about this. You asked, "what happened to him in those days"? In other words, he was physically there with Elise in 1912 as was shown by the registry book signature. Then he sees the coin from 1979. Did he just simply vanish into thin air before her?
As to why he stares at the coin and disappears, He had accidently placed a coin from 1979 in his vest pocket, when he pulls it out and sees the date it causes his mind to jump back to the future.