In general the fixtures don't require maintenance except for the test probes and gas springs.
Gas springs loose pressure over time (some years) due to gas leak and wear. A gas spring may be utilized for 30,000 times without notable change in use of the fixture.
A common specification by the manufactures for the test probes are some hundred thousands operations before the reliability is too low. Fixtures not utilizing true parallel motion makes more wear to the test probes reducing life time for the probes. The ATP fixtures utilize true parallel motion.
The most common test probes have self cleaning test probe heads. i.e. dirt and flux from solder don't build up on the test probe tips. If the probe tips any way are to be cleaned a brush can be used. Don't use any liquids (may penetrate the moving part of the probes).