We have several at my day job. I'd say we've had at least one for maybe 12 years. (Our original one was a used Hewlett-Packard, and we still have it and it works just fine.)
The worst one drifts about 3 ppm a year (for dcV). Some drift less than 1 ppm in that time. (I really do not track Ohms drift, although I could look it up.) We have a 3458A/002 and it doesn't do any better than some of the non-002 units. Most all would pass the 002 specifications if the artifact were performed once a year.
We don't track the (7 day) A3 drift. (Maybe we should.)
If one is OOT (after calibration) or giving errors, we will usually send it to Keysight.
Keysight likes to replace the calibration RAMs no matter what the problem is (I'm not sure why). The battery is in the RAMs, and therefore, to replace the battery the RAMs need to be replaced. We did send in one unit that would not pass at Zero Vdc (even after performing CAL 0) and the only thing they did was replace the calibration RAMs. (The unit would pass every other check.)
If a multislope rundown convergence error occurs, it is most always due to the A3 card (which is where the A/D converter is located). Error codes that tag along with this error will indicate what the 3458A was trying to do but may seem random because lots of functions use the A/D converter. If you replace this card yourself, then I would recommend inspecting the fiber-optic connections for foreign objects.
I've repaired several other things myself, such as replacing the display or terminal board or broken pushbuttons and associated hardware. (The six binding post terminal board is one unit, and is the same on both the front and rear.)