I strongly suspect you have abandonment issues which can be traced back to your childhood and possibly problems with your parents. In terms of how to deal with it, see my post on emotional investment which I will quote from a previous reply in February this year:
60yoc summed it up perfectly with his Zen way of looking at life: Every relationship ends. Either you break up or one of you dies. Accept that every relationship is temporary and you will be a lot happier. Every relationship is like a flower. Enjoy it while it blossoms and blooms but don't cling onto it when it dies. Breaking up with a girl is just the end of a chapter in the book of your life. Meeting women is easy. Remember that.
The key to getting your woman to respect you is equal investment.
Examples:
1) If you text her and she waits 3 hours to text back, do the same to her.
2) If you text her or message her 8 lines and she texts you back saying "Ok lol. Luv u too. C u soon

xxx" then stop sending her long messages
3) If you both live alone, don't travel to see her more often than she travels to see you.
4) Learn to say "no" to a woman sometimes. It's attractive.
5) What do you do when you're not with your girlfriend? What's your drive and ambition? If you lose your drive, you will lose your woman.
6) If you call her twice or more and she ignores you, ignore her when she calls you back.
7) If she threatens to leave you to get her own way, stay calm and let her go.
8] If you spend $200 on her birthday and she only spends $50 on yours, spend $50 on her next birthday. You get the idea. The relationship dynamic is actually very similar to the Push/Pull dynamic in pickup.