a gut strings lifetime... who knows? it is hard to predict it. it is like your shoes, depend by a lot of things.
However in my experience the most critical string is always the 1st (of course). If can last 10 days or till some months.
In any case, despite the beautiful sound, the gut setup is very expenisve, strings has raf surfaces, they less stable to moisture changes and last a less.
We are luky to live in these times...
Mimmo