What's only max 1 registration? The Max Simultaneous Devices in the SM profile? Or the registration policy in the settings file? It can be set to simultaneous or alternate and there's a 'max simultaneous' parameter in the settings file too.
So, if I had Core SM1, Core SM2 and BSM, I'd say "simultaneous" with "max" 3 but i could still have "max devices" at 1 in my SM profile and my 1 9600 phone would simultaneously register to Core SM1/2/BSM.
If I had a IPO or Audiocodes as a branch gateway, I'd do everything the same except say "max simultaneous" is '2' in the settings file. When the 9600 registers, it'll get SM1, SM2, and "survivability server" from the SM profile in it's PPM as it's 3 SIP registrars. BSM supports registration while on core SM1/2 but a IPO or Audiocodes don't, so if I told the phone it should simultaneously register to all 3, bad things would happen.
Conversely, if you got max devices 1 in your SM profile, and something about the SBC is confusing the fact that it's the same endpoint trying to simultaneously register rather than two different endpoints trying to register the same profile, that could explain why the phone's 2nd registration is successful but SM1 tells the phone that it's first registration has been logged out. Because the phone considers the two registrations to be to the same core, if it's told it's logged out from either, it'll just go back to a login screen.
Do the phones stay up OK on 2 SMs when on the LAN vs the SBC? If so, I'd say you look hard at the register messages on both sides of the SBC to SM1 and 2. There's something in there that would make the SMs consider them 2 registrations from 2 endpoints and not 2 registrations from the same endpoint.