How long do cycling shoes last?
On a road bike in Southern Californie, I ride 250-500 miles per month (rarely as much as 1000 miles/month) and I am still using a 6-year-old pair of Specialized (their highest-end road shoe with BOA closure system). That is the extreme, however, and they are beginning to show wear. I ride with a racing club and I would estimate that most of my club’s members replace their shoes every 2-3 years or so. But several of them are riding 1000 miles/month or more regularly. If you are a weekend warrior, I think you could make your shoes last 5-10 years with decent care.
And as the other answer points out, road shoes have an exposed cleat that wears out more rapidly than the shoe. I propably replace my cleats once a year (maybe every 4000 miles), but that only costs ~$25 and takes 5 minutes to swap them out.
All of this is dependant on buying high-end shoes. I have never bought low-end shoes so I can not vouch for those.
In my experience they are NOT like running shoes which are replaced with respect to mileage. I ride quite a lot, and with care get 2 years or more form shoes. But, I don’t walk around much in them, which makes a difference. The cleat is the part that often takes the abuse, and that can be replaced. I attached a link to a nice article about cycling shoes.