Yup. I'm able to connect much better now with the gigs. Some days better than others. Being in the zone as David mentioned still holds strong. Being able to emulate that emotion at the beginning will help get into the nature of the song a little more and then you end up being more connected, at least in my experience.
Regarding your question of keeping emotion every time while doing a song repeatedly, I got this tip from John. To be able to reassociate the emotion in the song to a current situation or a recent life event really helps.
At first this seemed a little difficult for me since my mind is used to associating the song to the original reason I wrote it for.
But then, a song is interpreted by every person in their own way. In fact that's the beauty of it which brings people together through the music. This works for the artist too. You just got to get out of the habitual way of thinking. I'm known for tearing up on stage quite often. That's because of all these tips and things I've learnt from other musicians.
Anyways, on a side note, there will be a new article about this - "Keeping Emotion" very soon. I'd interviewed John about this topic a while ago and being the editor, I added my own views a bit as well. This topic is super close to me and I look forward to publishing it soon.