I just want to be sure I understand the architecture here. It may ultimately prove irrelevant, but since I'm not sure what's causing the problem, I don't know what may or may not be useful in solving it.
Router #1 is the only device connected to the Internet (via its WAN). It is connected by a WDS link to Router #3 and Router #5. IOW, Router #1 has the MAC address of Router #3 and Router #5 in its WDS table, and each of those has the MAC address of Router #1 in their respective WDS tables.
You also have two WAPS (not really routers). WAP #2 and WAP #4 (what you call Router #2 and Router #4, respectively) have WDS links to Router #3. IOW, Router #3 has the MAC address of WAP #2 and WAP #4 in its WDS table, and each of those has the MAC address of Router #3 in their respective WDS tables.
I assume neither the WAN port of Router #3 or Router #5 is ever used (or else if they are, you feel it’s not relevant). So the only router that actually routes is Router #1. All the other routers and WAPs are really just bridges. Any device connected to any router or WAP is part of the same network (e.g., 192.168.1.x). You've kept DHCP enabled everywhere, but only Router #1 is authoritative. All the others simply act as relays.
For all intents and purposes, it's just one big, distributed network of wireless APs to which you can plug in any wired devices and gain Internet access or share files and printers on the local network.
Do I pretty much have the picture?
If so, the reason I’m reticent about RIP is that you only have one logical network (e.g., 192.168.1.x). You might possibly have a need for the STP protocol to prevent loopbacks if this was a WDS-based mesh network (which it isn’t). But as defined, it’s not an IP routing problem. It appears that you’re *hoping* that if RIP broadcasts are expected and not received, then the routers/WAPs will assume the WDS link is down and re-establish it. But I have no reason to assume that’s the case. I’m not saying it might not be the case, but I never would have assumed that myself.
So it begs the question, why would the WAPs behind Router #3 give a hoot about the temporary loss of the WDS link between Router #3 and Router #1. Those WAPS should be perfectly happy to continue their WDS links to Router #3 and any devices/services still accessible (obviously the Internet would not be one of them).
Something else is amiss here, and maybe it’s the WDS configuration itself. But WDS is pretty simple and basic, at least as far as end-user configuration.
I’d be curious to see what happens if wireless security is disabled. What are you using at the moment?
Another thing I would try (if practical) is place one of the routers (P660HW) behind Router #3 and see if it drops too (Router #5 looks like a good candidate). The reason I’m suggesting this is that WAP #2 and WAP #4 are different devices. WDS is notorious for incompatibilities. I frankly don’t trust it except when all the devices are absolutely identical. I’ve even seen devices you would ASSUME should be compatible prove otherwise, such as different devices but still from the same brand (like we have here). WDS can be a royal PITA unless you keep everything identical.
Again, I’m just speculating here, I have no proof of anything. But I’ve been dealing w/ WDS for many years and absolutely despise it. Because it’s not a wifi certified protocol, there’s no guarantee of compatibility across brands, and as I said, sometimes even within the same brand. So I’m always suspicious of its use except when conditions are perfect. That’s why I want to see what happens if you place the SAME device (P660HW) behind Router #3. If that device stays connected when Router #1 drops its connection to Router #3, I’d be willing to bet it’s a compatibility problem between the P660HW and WAP3205.