Just to let you know that you're not the only one, I'm seeing some issues with the built-in 5GHz as well. I have the 4GB RPi4 as part of a desktop kit I got from Vilros a few days ago.
My router produces 2.4GHz and 5GHz networks, and I've always had them as separate SSIDs so I could more easily "see" what was connected to what and to keep my wife/kids/friends on the network(s) that I want them on and no others, so my workaround for now is to setup my wpa_supplicant to include just the SSID for the (working) 2.4GHz network.
I've been using 5GHz with a few other devices (my phone, one laptop, etc.) for years now with this same router with zero problems and awesome speeds.
But my issues with RPi 4's internal 5GHz seem to mirror yours: it seems to be a crapshoot at reboot time, and even if it does miraculously connect, it drops out rather consistently .. and sometimes it may briefly magically reconnect and then it craps out quickly again. Much googling hasn't helped me too much, ostensibly because not too many folks are delving into the details of the Pi4 yet. But I've ruled several of the 'obvious' possible things out: it isn't IPv6 related (same behavior w/ or w/o it disabled), and it isn't heat-related (I have a fan attached to my case [I'm not using the stock case that came with the desktop kit precisely because it doesn't allow for adequate cooling] and a temperature monitor via 'watch' shows it consistently < 50C even when working 'really' hard), all country settings appear correct, no crazy errors being reported, and so on.
I'll post more as I learn more, but at least I have been able to prove to myself that it is stable (albeit at very low data rates it seems) when running at 2.4GHz ... but my 2.4GHz near where I live is horrible since it's so overcrowded (too many people == too many 2.4GHz wifi routers!), so I was (am!) really looking forward to getting the built-in 5GHz to work. My main use case at present for the Pi4 was to see if I could create a simple, fully wireless, put-it-anywhere-in-range, rsync target (ie, a type of simple NAS, if you'd like). In that regard, it only has two connections: the USB-C for power (5V/3A supply), and a SanDisk 500GB drive connected to one of the USB 2.0 ports with a short flexible USB cable (and eventually that Sandisk will be velcro-tape-attached to my case). I'm using stock Raspbian as installed by NOOBS, and I subsequently configured everything to run fully headless via direct ssh command line, with an option to turn on x11vnc (for remote initial login desktop access) and/or tightvncserver for virtual vnc access. I did that to further limit power consumption and heat since no HDMI signals are therefore in play, as both HDMIs are unconnected.
I attached a picture of my simple setup:
However, since going completely headless, I have not gone back to retest the 5GHz to see if there's any difference now that the HDMI is out of the picture. I can't imagine there would be any nefarious interaction between the two, but who knows. Eventually I'll retry it, but right now I'm in the middle of doing a ~3 day long-term-test just at 2.4GHz to continue to prove that out from a stability perspective. So far so good - I've transferred about 52G out of a planned 400GB or so for my initial rsync tests. I see a slight unexplained creep in swap space (it really shouldn't creep up at all given the nature of my test scheme, but it is) use during the continual transfer, but not much, and so I've been clearing out the page cache every 10GB or so just to play it safe (since my main goal right now is stressing the wifi + storage, as opposed to diagnosing the potential memory usage concern).
Anyhow, I'm hopeful that this can be solved, but if it can't be solved internally, there's still the nuclear option: go to an externally-powered 5GHz dongle via an external powered hub .. but that would really be a shame, and would limit the goal I'd set for a truly "small" low-power high-capacity NAS leveraging both 2.4GHz and 5GHz with just a USB-C power connection featuring the RPi4!