Why do couples stop doing this?
I think holding hands is the most basic and non-intrusive form of showing someone affection. I think it is something so small, that no couple should ever have an excuse not to do if their hands are not occupied with something else and they are walking with or sitting next to their significant other. I tend to pay attention to this a lot, being a newlywed, in couples older and wiser than myself...but what I've largely found is that they don't hold hands! Even young couples like my husband and I who have been together around 3 or so years don't do it! It's such a tiny statement of affection and possession, but no one does it anymore.
I once watched an entire theater exit a movie, as we were waiting to enter it, majority of them older or middle aged couples. I watched them walk from their theater, all the way down the hall to leave the building. NOT ONE couple grasped their partner's hands (one woman out of the crowd put her arm through his arm). Men had their hands in their pockets and the women just wandered along side. It was so sad - I just wanted to shout "Hold her hand! She's right there!"
I could go on and on about this subject...I feel very strongly about it. Maybe it's just me. Others maybe don't get anything from holding the hand of their loved one, but personally, it keeps me close to my husband. I feel connected to him without being intrusive and I like to let others know we belong together.
Maybe this is just a silly rant, but I urge those who are married to never stop holding the hand of your spouse. Don't let that fade with the newlywed stage. I feel like when you let those tiny affections fade, other small things go with it...and so much of what Tom and I have learned so far in our marriage, is that those little things are what really mean the most.