In online business, stable means 99.9% availability.
I was not a user, in fact, I am hearing about this service for the first time now, but if you are already referring to a previous domain, I assume that you want to stand behind the reputation that was built earlier, whatever it was.
However, can you somehow prove that the same people are behind the new, restarted site/name?
99.9% availability applies to active production uptime, not to intentionally scheduled downtime during infrastructure migration.
By that logic, every major provider that has ever migrated hardware, changed ASNs, rotated carriers, or rebuilt infrastructure would suddenly become “unstable.”
As for proving continuity: same backend structure, same command system, same routing logic, same operational model, same support channels, and existing users already recognized it before you did.
Usually when a service gets exit-scammed, the operators don’t come back publicly under the same branding and continue supporting the same network architecture. That would be a pretty inefficient scam.