The issue crops up for sure.. are you plugging ethernet into the TC?
Is the test by wireless?
A gen1 TC is now more than 4years old.. and likely to be suffering all kinds of issues.. Although it can happen on a new one.. it is difficult to know without using a replacement as a test.
Do a factory reset on the TC and see if setting up again has any impact at all. If not get another router.. any type and test again.. bridge the TC and see if it will still work just as a backup destination.