Wants affection then runs away

Our dog Khloe is a 4 year old beagle terrier, We got her at a shelter last summer. I don’t know her history but do know she was surrendered because they were moving. She was trained to the extent where she knows her name and knows to sit. She doesn’t need a leash when outside. So she listens well, she is not afraid of us. But it seems that she has anxiety. She will be laying on the couch, and look so sad, will make eye contact and look away. Will look sad,until I approach and pet her she lights up a bit,maybe a couple of wags. Only time she really gets excited is when we come home,food and going outside. But what prompted me to post is that she will beg for attention,to the point that she whimpers. if you pet her and stop she whimpers. And if you give her a lot of attention, when you stop she runs to the other couch or to her crate. I am just so confused on her behavior and it is discouraging to me. I feel like I either do something wrong or I’m ignoring her too much. She sleeps with us,she lays down next to us when we are home. I even thought that i could spoil her some. I started serving some canned food into her dry and giving more treats for excitement. What can I do or am doing wrong?

P.S. The running away instance just happened again maybe 10 minutes ago, that’s what prompted me to post, and now she is back to check things out and lay down.