It is obvious that one of two things is going wrong.
1 - The camera is failing intermittently.
2 - The cable is failing intermittently.
If you eliminate one, like the camera, it has to be the other, the cable. No one can diagnose what went wrong over the internet. Just the act of removing the camera could easily remove the intermittent cable problem. If you had a TDR and could actually "look" at the conductors it might be possible to figure out where the problem is physically, but a continuity tester has no way to determine that.
Re-terminating the camera end of the cable would be my first step, and I've done, easily, hundreds while on a ladder.
Here's a test I just did;
NO continuity tester receiver outdoors. Only the powered continuity tester indoors. I noticed that the little light for wire #4 barely illuminates with a quick "flash", ONLY when the RJ45 plug from this camera in question is connected. It's very difficult to see because it's so dim. What would this indicate? The flashing also doesn't seem to match the speed of the test light either which is weird.
I can't tell if #1, #2, or #3 are doing the same because unfortunately the light from the testeris somewhat visible. You wouldn't see it otherwise though because obviously when the tester and receiver are working together the signal light illuminates at full brightness.