Yeah, that looks like the down converter antenna, lucky you were able to get it. And I see the receiver is marked as 'Downconverter required'. So you're off to a good start
It's possible to convert the board to standard GPS (no downconverter) but it's not easy, and you need another receiver (practically unobtanium).
You say that it does track for a while and then loses the satellites. (And yes, those integer numbers on the bottom line are the tracked satellite numbers.) Apparently something is warming up and drifting, causing it to lose lock. I don't think the OCXO is required for GPS to get satellite fixes, but it would of course never go to locked state. FYI: All of my units have OCXO or Rb options and require them to be present or the system does not initialize. So I think you must have the TCXO version since it starts up OK.
Question: How do you know you are missing an OCXO?
Answers:
+) No, the PVC stub is not an absolute requirement.
+) Yes, proximity to metallic objects is detrimental to signal integrity. Best to place above and away from them, best as you can.
+) Yes, the firmware is obsolete
We're talking mid-90s here. That said, the unit should work (I have 4 of them, different build options) with the only real effect of the date/time being wrong, which you can fix with the FN68.
+) There are no changes to the almanac distribution
+) The default is to send the time every second
+) You probably aren't sending it the right commands. Have you read the fine manual?
+) AFAIK, there is no serial port lockout, but you can lock the keypad.
I doubt its the cause, but check FN65 and make sure all satellites are enabled.
If you're feeling adventurous, you could check the oscillators on the CPU board. These are under the GPS board. Actually there should be two. One a 16.368 MHz for the GPS clock, and a 10MHz TCXO. It's possible if the 16.368 oscillator is off frequency enough, it could cause poor sensitivity and other symptoms. I don't exactly recall 100% but I *think* the MCX connector closest to the board edge has this signal on it, the other one goes to the GPS antenna connector.
I also notice you have the NTP card. Are there other modules installed?