For a while she had held out hope he would show up in her time. Kagome reasoned InuYasha was a half demon and even though he may not lie as long as a full demon, his life had to be extended a reasonable amount of time to possibly make it to her on this side of the well. After a month had passed she had to face the fact he may not have survived this long. She felt only death would have kept him from her. The thought of him having died was like the well had closed all over again, squeezing her heart, stealing her breath, making her feel she might be dying as well.
It was all too much for Kagome to bear most days. First the well closed, separating her from InuYasha, and after he didn't come for her in her time, thinking he must have died. Some days she didn't go to school and it wasn't for a bogus illness her grandfather had made up. Her heart was simply too broken for her to face the world and she would sit by the well instead. Being 500 years in the future where InuYasha had already lived and died was worse than him being on the other side of the world.
InuYasha looked over the edge of the well as he did every morning before he set out to hunt for Kaede and every evening after the sun had set. It had been a year since the well closed and he stopped jumping in six months ago. He knew the magic was still there but it wouldn't let him pass. And if he couldn't get through he knew Kagome couldn't get through, either.
So, he kept vigil by the well. InuYasha would sleep in Goshinboku when the weather permitted or with Sango and Miroku or Kaede when it didn't. During the day he stayed busy helping the older miko or demon slaying with the monk. In his free time he could be found at the well. It was the closest he could be to her and he wasn't willing to leave it for long.
InuYasha often tried to dream up ways to get a message to Kagome. Something to let her know he was waiting. That he thought of her every day. No matter what he came up with, he couldn't see a way his message would survive 500 years to find her. Then he thought of coming to her in her time if he was still alive. That seemed the best he could do, aside of staying by the well in case it let her through again. Either way he would be waiting. Living 500 years in the past where four generations of Kagome's family didn't even exist yet was worse than being separated from her by Japan.