I'm not aware of classical music pieces that require some occasional retuning, but if they exist I suspect they are written specifically for a particular virtuoso performer who can pull it off reliably every time.
On the other hand, some virtuoso performers do exist, who among other things take advantage of the possibilities offered by the instrument's tuning machines. One example is this:
A similarly gifted guitarist, Luca Stricagnoli, occasionally does something like that, but I couldn't promptly find an example.
And while this isn't strictly an answer to your question, but to give an idea of what some people can do, I once saw Vishwa Mohan Bhatt change a broken string in the middle of a long improvisation and then tune it up as needed, and throughout this process not a single bad note was heard... in fact, if I had not been watching him, just by listening I could have thought that the improvisation just changed to a slow mood for a minute before going back to normal.
Bottom line, retuning while playing can be a thing, but only for the top of the top of players.