The following is even crazier than most of this website!
The 2000 km long reverse track does not support payloads, so the track envelope can have a large plenum above the rotor.
We will put a 50 cm diameter plenum above the rotor, and use that for a 2000 kilometer long rotor repair chamber, running from east station back to west station. During periodic maintenance, this chamber contains long, narrow track repair robots weighing 50 kg and carrying a segment of replacement rotor. The robot begins a 100 gee acceleration run at east station, reaching the rotor speed of 14000 m/s after a 100 km run. Additional velocity transformer boost coils help bring it up to full track speed. The robot clamps onto the top of the rotor, disconnects a balky segment, moves back, and inserts a replacement segment, as it travels 1800 kilometers east to west over two minutes. As it gets within 100 kilometers of west station, the robot begins a 100 gee deceleration, stopping at west station.
The robot is sent back to east station, to load another replacement rotor segment, at a more leisurely speed. Many repair robots may be operating at once on the westbound reverse track, if there is enough drive power for the loop. A 1 GW power plant can provide energy to launch two robots per minute; with two hours per day set aside for maintenance, 88000 rotor segments ( 1.5% of 5.6 million ) can be replaced per year. If rotor segments have a higher failure rate than that, the loop will probably need to be lowered, stopped, and repaired every few years. In time, the loop may be provided with more power, the robots made lighter, and possibly faster, so they can replace or patch more than one segment in two minutes.
The repair robots themselves must be highly reliable. If the robots fail to detach, they will likely bring down the launch loop, so there should be some mechanism to forcefully detach them near west station, perhaps associated with the high accelerations of the downwards curving deflection magnet.
If the robots fail to decelerate, they must be ported westbound out of west end and sent flying into interplanetary space with a velocity surplus over escape of 7690 m/s, retrograde to the earth's rotation. The orbits they end up in will depend on which direction west station is pointing, with a downwards deflection of 31 degrees or (2 hours). At 10pm they launch prograde to earth orbit, an elliptical orbit with apohelion beyond the asteroids. At 10am they launch retrograde, with perihelion near Mercury. In between, they launch into orbits up perihelion and apohelion bounding the earths orbit. Repair times should be chosen carefully, so these escape orbits do not intersect the earth or moon anytime in the near future, and preferably will hit Venus or Mars in one or two solar orbits. However, remember that the segments are designed to disintegrate when hitting air at high speed, so they will pose very low risk to people on the ground. The robots will be more solid, and more dangerous, but the risks will still be small.
Large Repairs and Scheduling Delays
Specialized "long" robots may be designed to replace dozens or even hundreds of segments at once. These will deplete the rotor of a lot of momentum, so launch operations must be delayed until the rotor is restored to full energy. Some payloads will miss their launch window, and have to be stored for a day at west station, or returned to the surface. However, this is better than risking the whole loop because of a long, bad section of rotor, perhaps damaged by a meteorite or a balky payload.
The rotor segments can be visually scanned every time they pass through the east end of the loop. A nanosecond pulse laser can illuminate 5 centimeters of rotor, making an image captured by CCD imager, such as the 7500 frame per second, 1Kx1K Protron camera. Assuming 6 cameras at 60 degree circumferential angles, 240 cameras and lasers can form an image of the entire moving rotor to 50 micron resolution in real time. The images can be stitched together in software, compared to previous images, and automatically evaluated for damage. Visually defective or otherwise misbehaving rotor segments can be scheduled for immediate replacement as they come back through east station.