Why is syncing so unreliable?

You wrote, "I have Connect configured to sync everything...".  I assume you meant Explore, rather than Connect.

Rather than synching everything, try synching to a primary collection.

You're right, I edited my post to fix the mistake.

The thing is, I don't want to sync some of my activities, I want to sync all of them.  And I don't want to have to do that manually. That seems like a reasonable expectation.

As a software engineer, I find it impossible to explain why the app sync reliably but then suddenly fails to do so for several days straight. The ability to sync reliably is core functionality.

If you choose synching to a primary collection, you will synch everything, but it will all go into one collection. 

You can later place what you synched into different collections.

But that doesn’t help with the existing activities that aren’t showing up in Explore, it would (at best) solve the problem for any new activities.

In the UI it literally says the easiest option is to sync everything. Except that doesn’t work, and using a collection is just a clumsy workaround that may or may not work for future activities.

I appreciate your suggestions but Garmin needs to fix this.

No, it should work for existing activities on your device and future recorded activities. 

Also, you want to ensure that any collections are not too large, as that will cause synching problems. The number of activities, waypoints, etc. are limited, though I don't recall the exact limits. A collection will have a yellow triangular warning symbol if one of the data fields is too large.

From https://support.garmin.com/en-US/?faq=Om0zJvBOJ2897CT2dvcFm5

 "If a connection issue occurs between the device and the Garmin Explore app while recording a GPS activity, and if the activity syncs to the Garmin Connect app successfully before the connection is restored, the activity will not be available in the Explore app. Similarly, if the Garmin is synced with Garmin Connect using Garmin Express before the connection is restored, the activity will not be available in the Garmin Explore app. For steps to resolve connection issues, see Related."

I found the collection limits, "Large collections usually contain over 100 waypoints, 20 routes, 5 tracks, or a track with over 10,000 points." Activities are not mentioned because activities were added to Explore after this was published. I don't know what the limit is for activities.

No, it should work for existing activities on your device and future recorded activities. 

It doesn't work for existing activities because they don't show up either in Explore iOS or Explore Web, so there is no way to add them to a collection.

Also, there is no yellow triangle in front of any activities -- they simply don't show up. Complexity shouldn't be the cause either, since significantly longer ones show up while ones with shorter tracks do not.

But have you switched from Synch Everything to Synch Selection (and then choose a primary collection)?

The yellow triangle would be associated with a collection, not an activity.

I have tried that, but I can't add the missing activities to the collection because they don't show up and are therefore not selectable.

If the missing activities uploaded to Connect Web, as your initial comment suggests, then you should be able to download them from Connect Web to your computer.

After downloading to your computer,  upload the activities into Explore Web. Then, using the Explore App, synch the app with Explore Web and they should show up on the app.