Do antimicrobial abilities of copper boilers decrease over time?
It is possible that the ability to release soluble copper ions could be reduced with age.
I am assuming, for example, that a very small amount of the cuprous oxide coating could react with, say, carbonic or hypochlorous acid (from chlorinated water) to create a poorly soluble basic salt.
However, with time, to quote a source, namely Handbook of Industrial Water Treatment, Boiler Water Systems, Chapter 12 Boiler Deposits: Occurence And Control Contact:

DEPOSITS:
Common feedwater contaminants that can form boiler deposits include calcium, magnesium, iron, copper, aluminum, silica, and (to a lesser extent) silt and oil. Most deposits can be classified as one of two types (Figure 12-1)...scale that crystallized directly onto tube surfaces
sludge deposits that precipitated elsewhere and were transported to the metal surface by the flowing water
Scale is formed by salts that have limited solubility but are not totally insoluble in boiler water. These salts reach the deposit site in a soluble form and precipitate when concentrated by evaporation. The precipitates formed usually have a fairly homogeneous composition and crystal structure.

So, this growing deposit could likely reduce the concentration of copper ions that in even micro quantities has been reported as having an oligodynamic effect.
For example, per a reference a 2011 work published in Applied Environmental Microbiology, Metallic Copper as an Antimicrobial Surface, to quote:

The antimicrobial activity of copper and copper alloys is now well established, and copper has recently been registered at the U.S. Environmental Protection Agency as the first solid antimicrobial material...In connection to these new applications of copper, it is important to understand the mechanism of contact killing since it may bear on central issues...

As to possible mechanics, the article further notes:

In these enzymes, copper serves as an electron donor/acceptor by alternating between the redox states Cu(I) and Cu(II) (15)... the redox properties of copper can also cause cellular damage. A number or mechanisms have been suggested. Reactive hydroxyl radicals can be generated in a Fenton-type reaction:


$\ce{ Cu+ + H2O2 -&gt; Cu++ + OH- + .OH}$ (1)


The extremely reactive hydroxyl radical can participate in a number of reactions detrimental to cellular molecules, such as the oxidation of proteins and lipids (45).

So at least partially, suspected Fenton-like properties of copper could contribute to its reputed antimicrobial properties. However, this requires a surface presence of either metal copper or cuprous salt, but a growing scale coating may be inhibiting to this action.