Periodic HTTPS issue on home network

Every so often, I am unable to access any site over HTTPS on any device on my home network for a little while. Often, restarting the router fixes it (but not always!). The issue has never lasted more than an hour or so. I guess technically, it's not even HTTPS, it's just any outgoing TCP connection to port 443. Or at least that's what it seems like: nc -z <any site's ip> 443 doesn't connect at all. DNS still works and regular HTTP still works.

Any idea what could be causing this and how to fix it?

I have a D-link dir-655 router, firmware version 2.11NA. I have a mix of all types of devices (linux, windows, mac, android, chromecast, xbox) on both wired and wireless connections, and all experience the same issue at the same time. I haven't noticed anything else coocurring with it, though thinking about it now, I recall it mostly happening around the same time of day.

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