I suffer from irrational break-up fear too. It sucks. Welcome to the club
Here's what's working for me (somewhat, because after 4 years, I still get anxious and restless every now and then, but the attacks seem not to last as long, and I seem to able to calm myself down much faster)
I don't think, actually, that break-up fear is irrational. After all, there is a possibility, always, that a relationship will end (either because you, or the other person, or you both, desire it to end).
For me, telling myself that my fears are irrational, doesn't work, because it feels like I am denying reality, and then when something real happens that is a sign that a break up is actually a possible reality (like when my BF started dating again) it hits me double as hard. While when I know, and realize, that all things can change and that like GG says all relationships have clock attached, it becomes easier to deal with reality.
And that, for me, makes it easier to start building trust and confidence. Also: I ask all my partners to reassure me of this: that they will let me know if they no longer want to be with me. Kind of 'no news is good news'
and I will ask them this again, every now and then, if I need the reassurance. I don;t think there's anything wrong with feeling fear sometimes and telling your partners you need reassurance, as long as it doesn't turn into needy and clingy and dependant behavior.