(1) If you see the colour and/or tone of your prints beginning to drift more than usual from the monitor sof-proof it's time to reprofile both the monitor and the printer/paper combination.
(2) Normally it is not necessary to reprofile between batches of inks and papers if you are using brands that have a solid reputation for consistency over time.
(3) Normally it is not necessary to reprofile for firmware updates, but there could be exceptions in which case it falls under (1).
(4) Normally software should be stable in its use of colour management; if a software update throws colours or tones off, all else equal, the software needs to be fixed, not the profiling - that was one lesson of the recent Adobe experience. Sometimes new software versions bring along different interpretations of the image before doing any editing - here I'm thinking of changes to process versions in Lightroom. Normally in these conditions one adapts one's editing practices, not the profiling, to the extent these fresh interpretations are not colour management-based, but image interpretation based.