I think that trust to a non addict is something that is understood as paramount to any r/s. It's not something I ever had to think about (in terms of whether I would behave in a trustworthy manner-- I just did bc it's who I am).
I spent YEARS trying to explain why honesty was important and a non negotiable to AH. Years. It was the root of pretty much every fight we had.
He rationalized being dishonest SO well that even I started to believe that my "black and white" thinking about honesty was unhealthy. He convinced me that honesty was negotiable and there were gray areas and I actually gave him CREDIT for lying "less". Insanity.
So, I really think that unless someone gets sober, and more importantly, does the searching moral inventory and really re-aligns their moral compass to grasp values like honesty the way non-addicts do, then no, there is no regaining trust.
I never saw my AH sober in mind or body for more than a few months at a time and he never wanted to make himself healthy and thus "uncomfortable" and honest. To him, honesty and my trusting him were things he didn't care about.
When we care more about trust and honesty than the addict, I think there's the answer about whether it's repairable. When both people place the same value on honesty and trust, then there is hope.