When the connection drops, can you still ping 8.8.8.8? 
No

Alternatively, could you run a tracert to see where the packets are being lost?
While connection is up:

```
traceroute -n 8.8.8.8                                                                                                               
traceroute to 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  * * *
 2  100.*.*.*  539.978 ms  540.260 ms  540.122 ms
 3  172.*.*.*  540.176 ms  540.133 ms  540.291 ms
 4  206.*.*.*  540.214 ms 206.224.70.4  540.404 ms 206.224.70.8  540.527 ms
 5  206.*.*.*  540.943 ms 206.224.69.254  540.214 ms 206.224.69.244  540.102 ms
 6  206.*.*.*  540.227 ms 206.224.64.137  20.793 ms  20.511 ms
 7  142.*.*.*  20.546 ms  32.486 ms 192.178.110.155  24.288 ms
 8  74.*.*.*  24.325 ms 142.250.46.167  32.630 ms 142.250.213.127  32.518 ms
 9  8.8.8.8  24.261 ms  24.505 ms  32.566 ms
```

While connection is down:
```
traceroute -n 8.8.8.8
traceroute to 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  * * *
 2  * * *
 3  * * *
 4  * * *
 5  * * *
 6  * * *
 7  * * *
 8  * * *
 9  * * *
10  * * *
11  * * *
12  * * *
13  * * *
14  * * *
15  * * *
16  * * *
17  * * *
18  * * *
19  * * *
20  * * *
21  * * *
22  * * *
23  * * *
24  * * *
25  * * *
26  * * *
27  * * *
28  * * *
29  * * *
30  * * *
```

We also recommend capturing a mirrored packet trace while the issue is occurring to better analyze the root cause

I tested with this setup:
port 1: WAN
port 3: laptop
port 5: problematic PC
Then I mirrored port 1 and 5 to port 3.
On the laptop I used tcpdump to inspect packets. I verified the mirror was working. I am capturing a ping from the PC to the laptop. As soon as it is back up, the mirror shows packets related to ping outside the network (i.e. ping 8.8.8.8). As soon as the connection drops, the packets disappear from the mirror.

You mentioned that manually reserving an IP address on this device resolves the issue.
Yes, but only Issue 1. And not al all when configured through the Omada controller.
I do also have to configure DNS servers to avoid using the router ip for DNS to resolve (on other devices this isn't necessary). Either on the client or via the web GUI (ping to 8.8.8.8 then works without the additional step of configuring DNS servers). 

At that point, is the device still connected behind the same gateway?
Yes

Additionally, have you tried connecting to a different network to see if the problem persists?
Yes, hotspot as well as various routers. It doesn't persist there and appears specific to the ER605.