I bought my 2004 Prius new and the auxiliary battery lasted until 2015. I bought a replacement from Toyota and it died after 3 1/2 years. Why did the original last 11 1/2 years and the next one only 3 1/2?
The AVERAGE life of a Lead/Acid battery is about 5 years, some last longer, some last shorter. Make sure you buy a battery with a 60 month prorated warranty and if it lasts longer then that, you got your moneys worth. If it last less then you get some money back on the prorated part and you still get your moneys worth. Other than your time getting another new battery, that is.
My original, on my 2005 Prius, lasted from then to until 2017. It has only been 2 years on this one so can't say how long it will last.
The usual things that cause a Lead/Acid battery to go is Heat/continually over working it or a really hot environment or shorts; excessive vibration/ usually cause by a loose/missing tie down (or maybe a lot of driving over wash board type roads; not keeping the fluids topped off (if it is not a service free type); plate shorting internally (usually caused by one of the above.
On my 2008 the battery lasted a little over 5 yrs. before replacement but my 2013 lasted just under 4 years and I got a replacement from Toyota (EXPENSIVE) and it lasted less than a year but they replaced it for nothing.
I have a 2013 Prius C and had to replace the 12V Auxiliary battery at 34,856 miles, which was under the 36K miles under warranty for this battery, but over the 3 year mark (unfortunately for me the 3 yr mark, came before the 36K mile mark).