So I did some more searching while waiting for a response to my question. I've decided to assign two of the HS105 a static lease on my router. I will see if that helps. The other two will have a dynamic leases for now. If using static leases solves the problem, I'll make them all static.

Update: So setting the devices to static lease doesn't seem to solve the problem. One of the the four HS105 is already offline, and it's one of the ones which is in the same room as my router. It is interesting that my HS107 has never had this problem but all four HS105 have.

Same problem here with both HS105 and just got two new HS103 plugs and all seem to intermittently disconnect from WiFi.  Have updated firmware, reset several times and even assigned static IPs on my router (TP-link Archer C7) and nothing seems to help.  I have several TP-link switches (HS200, HS210, HS220) that all keep their connection to the router, however, the plugs are missing the same kind of re-connection logic that the switches have.  I’m hoping that an upcoming firmware update will fix the problem.  PLEASE!

Same issue with 15 devices, all of them. 

HS-200, HS-220, HS-100, and HS-105s

More news, but still no solution.

I reported the problem to TP-Link technical support (email support) and also gave them a link to this discussion thread. They tend to believe there's a problem with my WiFi network. I do not feel the same. This was their response.

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I have checked the problem you posted on the forum. I am sorry to hear that you have problem on this product. Here are some suggestions for you first:
--Basically, -64dBm is not quite good for the smart home devices. Smart home device will work fine with a wireless environment where there the signal is -40~-50dBm. It is suggested to change different locations for the smart plugs and ensure the signal is good.
-- Please check if there is an update notification on the app. It it is, please update first: go to kasa app--settings--firmware update.
--Please check if there are too many devices connecting to your router wireless. And try to cut down on devices.

For further help, please feel free to let me know:
--What is the OS of your phone, iphone or android?
--Please send me screenshots on the remote control page of HS105 devices where there shows the signal strength, model, hardware, etc.
-- What is your TP-LINK account?
--What is the model of your home router?
--What is the version of your kasa app? (home page--about on kasa)

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The plug with the -64 dBm signal strength is the one which is the furthest away from my router. The 2 in the same room as router are -43 and -54 dBm, but even they lose connection.

I can understand devices losing their connection to the router. The real problem is that they do not reconnect to the router on their own. If I unplug them and plug them back in, they connect right away. 

I have an update to report.

For the past 2 days I've been keeping an eye on the plugs in the Kasa app and I've never seen them offline. They all seem to stay connected, or they are auto reconnecting. I don't really have an explanation for why they seem to be working now.

I know that after I gave all the plugs a static IP lease on my router, I still saw them go offline. Whenever one was offline I would unplug it and plug it in again. Maybe they all just needed that power cycle after I gave them static leases. Maybe the static lease change didn't happen until the plugs were rebooted. That just my guess. I can't be sure that's why they are working now. I also don't know whether I rebooted each plug only once after the static lease change.

I will continue to watch them for a few more days and report back.

Another update, but probably not really that helpful to most.

Last night something happened to my router around 3:30am; I know the time because Nest sent me an email. When I woke up in the morning almost all the WiFi devices in my house were offline and were not reconnecting; not just the TP-Link devices, even my Nest doorbell and ecobee thermostats were offline. Only a couple of devices were connected on WiFi, such as my cell phone and a laptop. I rebooted the router and all the devices, including all HS105, automatically reconnected. I have no idea what happened with the router.

And despite the issues I have had with the HS105, today I ordered 2 HS200 switches. I hope to install them as soon as they arrive.

As a result of the router issue, the uptime not starts at 7:30am today.