Just because a channel doesn't "need" a tuning adapter, often when a TA is present, it still requires communications with the the TA to tune the channel as it "controls" the channel map. If mine goes down (usually with a flashing front light), I can't tune anything.
As to your original problem, I would probably ask this over on the SD forum. The fact that one tuner is still working probably makes this harder. You seem to indicate that the computer goes to sleep since you mention you have set the ethernet port set to not go to sleep. How does it perform if the computer never goes to sleep? It may be, as you surmised, that when waking up, it doesn't detect the tuners and "permanently" skips them. Occasionally when things are brought back from sleep, and even when starting from a reboot or power on, some things aren't ready as quickly as others and it may be that during this time it checks for the first tuner, doesn't find it, checks for the second, doesn't find it , then finally when it checks the 3rd tuner, the connection is available and it works. Some routers are just fine without the switch, its just been found out that some do touch the "local" traffic and can cause problems so I would still try it with the router (provided pc is wired to router, and if it is not, that may be part of the problem, especially if you are bridging these connections) . Last I heard their latest beta had an issue and until that is cleared up, I wouldn't update but the beta prior to that worked real well for most that were losing tuners. SD often "recommends" away mode over sleep but for some away mode ends up using more power than just leaving the computer on.
Do you have a dhcp server (with an address reservation for the prime to always get the same address)... the 169.254.x.x addresses of apipa are sometimes flaky but that wouldn't really explain losing only 1 or 2 tuners, though if there is an established connection it may be just not allowing new connections. If my TA goes out, it appears to control all chanels, not just those used by sdv