@IronRod 

The release notes for the A7 do not indicate that you are not able to roll back firmware so I would t try that. You might need to configure the router again as the setting may be reset. If you roll back the firmware and the issues disappear let me know.

@Tony Thanks for the reply.  This morning, I rolled back the C7 router to the previous version (3.15.2 build 170525).  This is what I was running successfully before the upgrade.  The good news is that, so far, the issue has not manifested after 5hrs of runtime.

Steps I took for the rollback:

1. Reverted the firmware and rebooted.
2. Changed the router login credentials.
3. Reset to factory defaults and rebooted.
4. Updated the security on the main WiFI with my names and passwords.  No other changes were made.
5. Rebooted the router.
6. Confirmed ability to retrieve data with the apps in question.
7. Updated the security on the guest WiFi with my names.  At this point, I have left security disabled.
8. Enabled the guest SSIDs.
9. Rebooted the router.
10. Confirmed ability to retrieve data with the apps in question.

I'll give this a couple days before adding my DHCP reservations.  I will report back here with the results.  Note that, on the AP, I still have the guest WiFi disabled.  I have only enabled it on the router.

@Tony Well, I just checked after completing the prior post and it has happened again. :-(  I checked before starting that post and all was well.  So, I again disabled the guest WiFi on the router. :-(  I'll see if I if/when I have to reboot the router again and report back.

UPDATE: A few hours later, I had to reboot again.  This time, I took the AP out of the wireless equation (disabled its radios).  Just trying to reduce the variables.  It appears now that it doesn't have anything to do with the guest WiFI as those are disabled on the router.  So, only the router is running main WiFi (2.4/5), no guest WiFi, and the AP radios are shut down.  I just rebooted the router again and rebooted the AP, to clear everything.  I'll see what it does now.

So, right now, when it happens, if I reboot the router, everything is great following the reboot and then, some hours later, they go sideways again.

UPDATE: Well, it appears that any conflict with the guest WiFi was misleading.  All the guest WiFi is disabled, but I just had it happen again.  The only thing that seems to clear it up is a reboot of the router.  That lasts for a little while and then the issue appears again.

Any ideas?

@IronRod 

What are the apps you are mainly seeing no communication happening on?

Since you have the A7, have you tried placing that as the main router rather than the C7?

In going back to the C7 being the main router, what you can try is to disable hardware NAT (not NAT). A user has an issue with using PPPoE and hardware NAT was getting in the way. Not your exact situation, but may help.

Another thing to try is to change the WAN DNS servers the main router is using. 

@Tony My next step was to swap out the C7 with the A7 today and try testing with it.  So, great suggestion.  (The C7 was purchased four years old (not old, certainly) but the A7 was purchased just last year.)

It is just strange that: 1) this disappears for a few hours after a router reboot, and 2) it only affects some apps but not all apps.  It is not a general internet speed issue as cabled connections appear to be unaffected and speed test always report expected speeds despite the issues with the apps.

Regarding DNS:  Before all of this, I had been using Cloudflare DNS servers (1.1.1.1).  However, with the recent factory reset, I had left everything at the defaults as much as possible (trying to minimize variables).  I just now set them back to Cloudflare DNS.

But, I also have an update on the testing:  I've found that these apps (listed below) aren't completely hanging, they just become really slow at retrieving data.  If I just leave them for a while, they eventually show the data.  The affected apps all require authentication with my account but not all require me to reenter them every time.  For those that do require re-entry, the authentication appears to succeed (the login screen closes) and then it sits on the main screen waiting for data. 

Apps exhibit the issue (with times):
Weather Underground (1 min 15 sec for the radar map to populate, another 15 sec for rest of the data)
Remember The Milk (tasks; about 2 min 50 seconds for the sync to finish)
Personal Capital (account data; about 1 min data to appear after authentication)
US Bank (accounts; take about 4 min for data to appear after authentication)
WSJ (news; the text appears but ads/photos/thumbnails don't appear until about 1 min 15 sec)
Google Books (store access; text appears after about 15 sec but images/thumbnails not until about 35 sec)

Goo

Apps that do NOT exhibit the issue:
Google Chrome

Google Mail
Google Maps

Google Photos
Google Play (updates)
Samsung Calendar
Textra (MMS)
Chase (accounts)
Amazon Kindle (store)
Amazon Shopping
Netflix
YouTube

Ride with GPS

Goodreads

@Tony This morning, I swapped out the C7 and replaced it with the other new-in-the-box A7 I had.  I just did the basic setup -- giving the WiFi my SSIDs and passwords, and just taking defaults on everything else (for now).  Thought is indicates a firmware upgrade is available, I have not done that yet.

The good news is that it seems to have resolved the situation.  It's been 10 hours and I've not had the issue manifest once yet.  That is unusual given previous behavior but I'm going to leave it like this for at least another 24 hours before I declare victory.  Then, I'll try adding things in to take it back to my original configuration.

P.S. I was delayed in making the swap as our ISP began having DNS issues early Saturday morning and they weren't corrected until early Sunday morning.  I was hoping that their correcting this issue might clear things up for me, too, though I really doubted it would.  And it didn't; it just made me wait longer to try my next steps.

@IronRod 

Thank you for all the detailed information.

Great to hear the A7 seems to be doing its job (so far).

@Tony I'm calling a victory.  My network is now back up as it was before (save for any DHCP reservations which I'll do later).  I've got the AP and all the guest networks running, all devices connected, and none of the suspect apps are exhibting any of the noted issue.

So, not sure what happened but, clearly, the C7 was having issues.  I appreciate your suggestions and responses.  It's always helpful to know that someone is actually listening. :-)

NOTE: I updated the title of the original post to better reflect what was actually the issue being exhibited