By "stale" I presume you mean can a dichroic filter change color, presumably after being heated.
The answer is no. Dichroic filters are made by depositing an inert material (typically a transparently-thin layer of titanium dioxide) onto a glass surface. The color of the filter comes from the interference patterns made by specific colors of white light as it crosses the thin-layer boundries. For example, a magenta filter will pass magenta and reflect green, the cyan filter will pass cyan and reflect red, the yellow filter will pass yellow and reflect blue.
Only by changing the thickness of the layer will the color change, and glass nor TiO2 will evaporate at enlarger-bulb temperatures.
Dust and scratches can obscure the filter, having some effect of the overall color balance of light, but the color of the filters should be quite stable. By the way, never touch a dichroic filter. The materials are very stable and ineret, and can be cleaned with good solvents, but while it may be necessary to dust occasionally with dust-off, the filters are best left undisturbed.
The largest cause of color head trouble is miscalibration of the filter raising mechanism. The more you dial a filter in, the more it is raised into the light path (they follow sequentially). If the mechanism has slack, or if it's received a good bump, it's likely that the color balance of the head set at, say, 20Y20M will look different than another head set similarly.
Of course I can say the same thing about two brand new heads from the same maker, just smaller differences.