What is the average lifespan of a phono cartridge?

There are a lot of variable involved. Cheaper cartridges use synthetic diamonds that don't last nearly as long as premium styli that are carefully cut and mounted so that the crystal structure is oriented properly to minimize wear.

How the user handles records and cartridges will also matter. If records and styli are kept clean, they last longer. According to one manufacturer (Benz or VdH, styli can last as long as 2,500 hours if the records are kept clean). I've used Lyra cartridges for close to 2,000 hours with no problems or sign of deterioration in tracking ability.

The rubber suspension parts of cartridges can go bad from aging and exposure to environmental agents (primarily ozone). So, even if unused, a cartridge could go bad. That is the theory, but, I've personally never encountered such problems--I've heard very old cartridges that still sound good after long storage.

My way of determining when a cartridge is beginning to go bad is to find the very few records that are challenging to track properly and listening for changes in the ability to handle the very few spots where distortion can be heard when everything is less than optimal.

When a stylus is worn, or the suspension has begun to fail, it will not track as cleanly as before.  This is first evident on more difficult to track passages, such as when a female vocalist its a not really hard or gets a bit too close to the microphone.  When you start to notice this sort of change, and cleaning the stylus does not cure the problem, it is time for a replacement.  It is NOT the case that slight, occasional mis-tracking from wear will ruin the record; records are not as delicate as some would make them out to be.  

There is no really good way to determine the extent of wear other than listening for it.  Visual inspection is nearly impossible to do right; often a visual check will not show wear or other problems that are quite evident from just listening.  

It is possible to trace a different part of the groove and mitigate at least some groove damage; I've heard this myself.  When a record is damaged by mis-tracking or a bad stylus, chunks of vinyl are removed so that the wall becomes pitted, it is possible to avoid these pits by contacting the groove above and below that area.  When a record is played, the stylus deforms the groove slightly, but because vinyl is highly elastic, it snaps back to its original shape.  The pits will affect how the groove deforms, so even though a different stylus might not be tracing the pits, the absence of vinyl will affect how the groove deforms, so, in that sense, the pitting cannot be totally avoided unless one uses a system like the ELP laser table.  I saw a demonstration of that table where a severely worn record was played with the laser focused at different groove depth--when the laser avoided the damaged part of the groove the record sounded like it was new.