Hi, I think you need to clarify/confirm what is actually happening.
Is it that the agents are losing their connectivity from Finesse A (for example) every few hours and they are failing over to Finesse B, which could point to connectivity type issues between the offices and your data centers.
OR is it that the Finesse server itself is having an issue and A is going down/not available.
OR are both Finesse going out of service where this could be more of a PG type issue.
Basically, first thing you should check is when this issue happens does it impact all users, only certain ones, only certain locations, do they lose all applications or only Finesse, etc., and that will help point you in the right direction.