In this scenario, after extensive testing we have found that the limitation is with the connection providers and banking institutions. The crux of the malfunctioning connection stability is the fact that there are two Synchronization records pinging the same banking institution login. One connection is pinging on behalf of One Company and another connection is pinging on behalf of Company Two. In rare cases, this may trigger the bank's security protocols and force the disconnection of one of the synchronization records. There is significant variability between banking institutions and between connection providers (plaid, yodlee, etc) but this configuration poses risk to connection stability. In this scenario, reach out to Odoo support to communicate that a ticket should be opened with the connection provider (yodlee etc) as it is unexpected behavior.

Aside from this limitation, in this scenario, the client has configured their system correctly. All accounts for a single banking institution and for One Company all linked to their respective journals on the synchronization record. 

Outside of troubleshooting directly with the connection provider, the recommended solution to address these limitations would be to separate the login credentials for each company's accounts. That is, keeping account 1 and account 2 on a single Bank Institution login and migrating account 3 to another Bank Institution login. 

Other than this, manually importing bank statements or repeatedly reconnecting the accounts would be the only other workarounds.