How to break our Our apology cycle?

So my girl is very caring overall towards me and I care for her too. One thing just wanna share with you, in case you understand things better than me - she many a times acts very rude towards me for things I couldn't have helped (for example letting her hang loose when some urgent work thing came up). I do understand what she might have felt, and I apologise and tell her that I'll make up for this. Then when she cools down... she starts apologising a lot.. Feels guilty of being the Bad One.. And all that.. I say it's not (as I believe emotions may get really out of logic sometimes, it's okay). But then while I'm trying to make her feel good.. Some other things crop up (my work hours are very scattered due to my profession) and
... She gets mad again. I don't completely blame her.. I apologise again and the cycle continues... .. And all of our free time goes into this. Any suggestion folks?
How to break our Our apology cycle?
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