I also remember my younger days when the thought of losing my girlfriend was incredibly painful, and it made no sense, because she seemed very faithful and devoted. But that did not stop me from feeling intense fear and loneliness when I thought that she might get tired of me. No matter how much I tried to convince myself I had nothing to worry about, the fear would keep cropping up.
With time, I lost my girlfriend, and eventually found other girlfriends who I equally adored. But the fear of being abandoned followed me from girlfriend and girlfriend. Knowing that I could survive the loss of a special person somehow had no effect on the fear I had about losing my present girlfriend.
It wasn’t until much later in life that learnt how to control this terror that would gnaw in the pit of my stomach. I still hate losing special people, but I no longer live with the terrible dread. I have taught the fear to go to sleep, and know how to keep it asleep. When I lose people, I know I will be sad. But it’s a sort of a peaceful sadness, and that’s OK.
If you are interested you might try following this simple suggestion:
The strategy I use, and have taught to many people, is very similar to some of the other answers to this question, such as facing your fear, passive acceptance, or learning how to move on. This following exercise take about 20 minutes a day for a couple of weeks. It requires a bit of discipline, but not too much.
The technique is often called Imaginal Flooding, and it is very useful in taking the power from any kind of uncomfortable obsession. Learn how to do it here.