Because I map this drive in windows explorer I would like to keep it at 192.168.0.125
Is there anyway to keep the LS220 address at an unchanging address like 192.168.0.125 ?
You would need to set a static IP, which you have done.
Also, you can map drives with the NAS hostname (machine name), instead of the IP. That probably would be better anyway, it would completely avoid IP address changes.
As to the time problems:
Given the various bugs that exist with the LS220 series, I would not be surprised if one or both of these things are because of firmware bugs.
I am using that same time server: ntp.jst.mffeed.ad.jp with automatic settings on my terastation, and have not encountered that issue with the time server. I don't use the sleep modes.
What is the DHCP pool range for your archer router?
The reservation sounds fine, but I would suggest to use a static IP address that is not in the pool range.
My router uses 192.168.x.100 to 192.168.x.150 for DHCP.
I assign static IPs to my terastations that are outside of that 100 to 150 range.
Ethernet Frame size is at the default: 1500 bytes
Gateway - router internal address
DNS - router internal address
I wonder if your NAS is having problems resolving DNS.
Some DNS servers don't like 3rd party DNS queries (if a host is not part of a network, it won't resolve the address. The DNS server will just reject the request of the outside host).
Try changing the DNS IP to your archer gateway IP, and set the time server to automatic again with the sleep timer off as a test. This way you can at least see what is going on with the time server.
If it works, turn the sleep timer on.
I'm surprised the sleep timer would start acting up just because of daylight time. Maybe getting the time server back on automatic settings- will resolve that.