Would u stay with someone who accuses u of cheating repeatedly&never apologises cos he believes u did?

I've never cheated on him and if i ever did i would of told as soon as it happened. The friend he accuses me of doing something with i've known for ten years and actually find quite horrid even tho the friend i know kinda has feelings for me.. One of the times i was pregnant and because i took too long going for a drive with my mate to get something for my other half (because he has a car and license and my fiance doesn't) i was accused of doing something with him.. Really sick of this ****. Any advice on how i can convince him or finally put an end to this crap?