That's the blip-to-scan issue. Radars could "see" them (as in, get a return from them), but the images on the displays relied on the target being in roughly the same spot on the display for consecutive sweeps to generate a bright "blip". If the target moved fast enough relative to the sweep rate, the resulting "blip" would show up as a faint streak of multiple distinct returns rather than a bright blip -- often faint enough to fade into the background and thus "invisibility".
Improved radars, and computerized image processing replacing the use of the cathode ray tube display itself for the processing, solved the blip-to-scan problem.
That makes zero difference to the guidance system that is using an analog computer to do the guidance. The operator simply selects the target and locks the fire control onto that target. In most cases, the fire control radar is conical scan with a very high PRF, or a monopulse with a high PRF, and in some cases continuous wave. In all three cases the pulse repetition frequency is so high it makes no difference against an aircraft. They can all track one without difficulty. Slew rates for radars even in the 50's was sufficient to keep up with most aircraft.
The problem comes when the analog computer time between calculations is in seconds and it takes so long to run the calculation that by the time it's finished, the system produces an error. That is, the computers were so slow back then that they couldn't keep up with very fast targets. A very fast plane at high altitude in the late mid to late 50's could literally outrun the computer.
Although beam riders couldn't really take on high altitude targets at long range, they could easily track a medium or lower altitude very fast plane and their engagement envelope was limited by the gather time for the missile, its relatively short range, and the speed of the missile itself.
An example of how this worked would be Nike Ajax. The time between guidance updates is about 5 seconds. That's how slow the analog computer used at the time was. Against a Lockheed X-7 drone, the missile system simply couldn't keep up with the speed of the target. It could track it just fine, but the computer couldn't tell the missile where to go to hit it because by the time it made the calculation, the missile wasn't where it was calculated to be. (The US Army actually hushed this whole thing up and classified it because it was a huge embarrassment).
The tour de force SAM system of the early to mid-50's was the S-25 Berkut system around Moscow. That shows you what having unlimited funds can buy! Each missile site could locate and track 6 targets simultaneously with its single pair of TWS Yo-Yo radars. These were tied into 6 analog computers each controlling one missile in flight to a target. For the time period, it was an amazing system.
Problem was it cost a national fortune to build it. The system made the Manhattan Project look downright cheap. This is something to keep in mind when building large ships and military forces in Traveller for wargame type scenarios. Even the polities in the game don't have unlimited cash...
The two have a six segment beam as they rotate that forms an X in the sky that marks the target. Each segment tracks a separate target feeding to a separate computer.