Having a young family is an exhausting challenging frustrating amazing beautiful rewarding roller coaster ride. This is my take without knowing your situation:
Your wife is probably at the permanently exhausted stage - giving all her energy to the number 1 priority - your three beautiful children. That will get better but you will both require heaps of patience and understanding.
I’d recommend you focus on expressing the love you have in practical supportive terms. The first being acknowledging how much hard work raising three kids is for both of you. If you can - arrange for her to have some truly free time alone or with friends every week- preferably away from home. Let her know you have everything covered. Allow her to regroup herself as a woman and individual. It’s hard to go from changing nappies and wiping snot, juggling laundry and meal prep and feeling permanently tired to a sexual being without a break in between.
Try to have some time just the two of you to catch up and talk every day and try to really listen.
Try to do something that you enjoy together kid free every week or two to keep the adult connection. (Easier said than done)
Reassure her that your affectionate advances are not always a precursor to sex. Show this by giving lots of hugs and kisses when there is clearly no sexual intent - will help to keep the physical connection.
Once the newborn fog and exhaustion lifts it will get better.
