How long do university libraries keep old copies of dissertations? How can I get a copy of a dissertation that I need for my research?
I suspect that that differs from university to university, and country to country, but I would not be surprised if the answer is "for as long as they can preserve the paper". I remember finding the master's thesis of my (fairly old) teacher when I was a high-school student.

On the other hand, it may be the policy of some university / library to digitalize them  (or in the old days, to put them on microfilm) after a given amount of time to save space in the library. This depends on how much money / time they have for that effort, and how much space they have in the library. It is easy to imagine huge differences between universities and countries in these different costs, resulting in different policies.

Regardless, you should expect that people will be able to find your dissertation for as long as you live (and afterwards).