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The Smithsonian Magazine article Lost Soviet Reflector Found on the Moon says:

There are actually five retroreflectors on the Moon: three placed by Apollo astronauts and two that sit atop Soviet rovers. But only one of the Soviet reflectors could be used by astronomers; the other, on board Lunokhod 1, the first robotic rover to traverse the Moon, was lost in 1971. Over the decades astronomers occasionally looked for the rover but without success. Even with the best telescopes it's difficult to spot something from here on Earth that's less than eight feet in length; the atmosphere interferes. And Hubble and other space telescopes aren't able to image the Moon in detail either.

Question: How did Lunokhod 1 become lost in 1971; in what ways did astronomers "look for it" after that, by earth-bound telescopes? With the Hubble or other space telescopes? Radiotelescopes/Radar?

Did it continue to drive after contact was lost? Or perhaps it's location was already uncertain before that?

A team called APOLLO (Apache Point Observatory Lunar Laser-ranging Operation), led by Tom Murphy, professor at UC San Diego uses the lunar retroreflectors.

Murphy said his team had occasionally looked for the Lunokhod 1 reflector over the last two years, but faced tall odds against finding it until recently. ...

"It turns out we were searching around a position miles from the rover," said Murphy. "We could only search one football-field-sized region at a time."

They were searching by aiming their laser at the moon and looking for reflections. But the system is set to only detect photons in a very narrow range of distances (~10 m) so searching this way takes a long time. This is called a range gate: only photons arriving within a timeslot that corresponds to 10-80 m of range are accepted; this helps eliminate spurious photons (random reflections off the moon's surface, etc), but means you can only search in a tiny space at a time.

The position of Lunokhod 1 was known to some extent, but that position had an accuracy of about 5 km.

The position of the Lunokhod 1 rover was known to within approximately 5 km (Stooke, 2005). This large uncertainty was a problem for LLR (Lunar laser ranging), which typically uses a narrow time window to reduce the inevitable background.

For example, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO: Murphy et al., 2008) normally employs a 100 ns detector gate, translating to a one-way range window with a depth of 15 m. Because the lunar surface normal at L1 is angled 50° to the line of sight from Earth, the range window maps to a 20 m wide band on the lunar surface. Positional uncertainty of a few kilometers translates into a vast search space so that detecting the reflector is unlikely. Nonetheless, APOLLO spent a small fraction of its telescope time on favorable nights unsuccessfully exploring the space around the best-guess coordinates of Stooke (2005).

The coordinates obtained by the LROC team had an uncertainty of about 100 m (Plescia, J., private communication, 24 March 2010) and were centered on a region almost 5 km from the previous best estimate.

Additionally, laser altimetry from the Lunar Orbiter Laser Altimeter (LOLA: Smith et al., 2010) on board LRO determined the site radius to better than 5 m (Neumann, G.A., private communication, 24 March 2010). But it was not possible to know if L1 was correctly oriented toward the Earth. A few unsuccessful ranging attempts were made in late March in unfavorable observing conditions. The first available favorable observing time on 2010 April 22 yielded immediate results, revealing a return that appeared 270 ns later than our prediction. The initial return was surprisingly bright, far surpassing the best-ever return signal from the twin reflector on Lunokhod 2.

With the laser ranging results, Lunokhod 1's position is now known to within a few cm.

The rover's position was "lost" during the mission, perhaps as early as after the first lunar night.

Parked during lunar nights to allow ranging attempts

- Soviets and French both got returns December 1970, on first lunar night

- But both failed in later attempts, even after end of mission

- Americans (at McDonald 2.7 m) never convincingly found it

So radio contact was still there and the rover was still operational (it would operate for almost a year!), they just couldn't ping it via laser any more.

I haven't found a clear explanation for why laser ranging was unsuccessful later in the mission.

There will have been some uncertainty in the rover's position.

Radio direction finding from Earth can give an initial position estimate, but isn't really accurate. Radar doesn't help because you can't differentiate the Lunokhod from background clutter. The Luna spacecraft sent photos after landing, but I haven't found photos taken during descent (which would have helped get a good position estimate).

The rover contained an inertial navigation system, but that will drift over time. And the only reference they had were photos from Moon orbit. Before LRO, resolution on those wasn't great so I can see how it'd be difficult to match photos taken by the Lunokhod with photos from orbit.

Also, if the original teams used tight range gates like the APOLLO team, it would mean small error in the elevation model could put the rover just outside the range gate.

Or maybe the rover was parked at an unfavorable angle relative to Earth?

If the rover azimuth were off by as much as 40°, no return would be possible

the Lunokhods had to be parked to optimize for early-morning sunlight on the solar panels, this conflicted with reflector placement.

According to the statement of the rover controller V.G. Dovgan both rovers are parked oriented toward the east. V.G. Dovgan explained this orientation by a necessity to charge the accumulator battery by solar energy after a two-week night without any maneuvering

In the end the Lunokhod was found via brute force, by examining LRO photos of the area by hand.

Then the APOLLO team tried laser ranging again, using a modified laser ("wide-gate capability") to increase the detection range of each shot from 10 to 80 m. This time, they received a clear reflection from the Lunokhod.

The landing site of Lunokhod-1 was well known, but it is a rover. It continued to operate for a considerable amount of time after landing, and like much data from Soviet Russia, data is difficult to come across. Hobbes has already mentioned how the attempt to find it went. The uncertainty estimates were about 5 km, making it very difficult to find with a 10m resolution.

The 10 m resolution is in range, and partially location. Due to the location of the rover, the range can vary quite a bit as one moves further away from the Earth, so a very precise knowledge of its location is important. See also this paper.

The opinion of Russian scientists about the "discovery" of Lunokhods were published in 2010.
Soviet scientists never "lost" "Lunokhod-2" - Academician Marov
https://ria.ru/20100317/214985144.html

Canadian astronomer incorrectly determined the position of the "Lunokhod"
https://ria.ru/20100319/215301851.html

Bazilevsky, after academician Mikhail Marov, repeated that no one had lost the Lunokhods.

“Their location on the Moon was determined by ballistics from the Institute of Applied Mathematics of the USSR Academy of Sciences, TsNIIMASH and NPO Lavochkin, which ensured their landing on the Moon. We did not know the accuracy of these definitions. There were only estimates. But the fact that they were quickly found in the new American images, speaks of the fairly high accuracy of these old definitions ", - said the agency interlocutor.