Like most constant fears, this isn't really about your parents so much as it is about you. You're afraid of losing them in some way, and below that, there's a fear of being alone, or of being abandoned, and probably some other things that only you will be able to uncover.
In the case of continual fear, the best way to relieve it is to find the root of it and pull that out. That can take quite some time, of course, but it's worth the effort. Being captive to fear is a terrible way to live. (And I say all this as someone who spent most of her life being afraid.)