It appears the TP-Link TL-WR710N router was indeed the culprit. The laptop and tablet were connecting perfectly to the wireless, but the LAN port on the router appears to be bad, although maybe I ran into 2-3 bad cables. I had a Buffalo WZR-300HP that I had burned with DD-WRT and set it up as a client bridge to the rest of the network. We can now ping the OpenSprinkler with no packet loss. Our logistical issue is that the sprinkler station Karen replaced was in the detached garage. I don’t have an Ethernet cable that long and have not run conduit to it yet. Once she had it wired up, she was disinclined to move it. The OpenSprinkler unit did not want to communicate using the IP it had previously received from the TP-Link when I connected it directly to the laptop. I was about to try and set a static IP on the OpenSprinkler (not sure how to do that), when I remembered the Buffalo.
We have run into a couple of other issues (NTP), but I will try to resolve them. For some reason, the NTP Sync feature is not finding a server. Combined with the intermittent packets, it would just hang, so we were disabling it. When Karen was disabling it, somehow the HTTP port got set to 0. Using the B3 options button, we could not reset the port back to 80, so we reset the firmware. That fixed the HTTP port, but reset the NTP Sync to enabled. Fortunately, with proper network traffic, there is a delay, but the device is not frozen. Karen likes the mobile app, but as a business analyst, she has already identified some enhancements. Perhaps I can take a SWAG at them and post the patches. Thank you again.