Do climbing shoes shrink?

Climbing shoes normally do not shrink, they actually stretch and get looser.
The amount at which they stretch depends on the material the shoe is made of, and of course, on how often the shoe is used. If climbing shoes are rarely used, or used not frequently, they will take much longer to actually stretch.

The material the climbing shoes are made of plays an important role in how much the shoes actually stretch. Leather shoes tend to stretch quite a bit, which is part of the reason why many climbers buy shoes that are smaller than their actual climbing shoe size, since they know that after some time, the shoes will stretch and will be a good fit.

Climbing shoes that are synthetic and not leather tend to either not stretch at all, or stretch very little. I have quite a few pairs of non-leather climbing shoes, and I cannot say that I have noticed any stretching in the shoes, and I climb 3-4 times a week. They still feel as tight as the day I bought them, just used.