Which OSI model layer is responsible for keeping open a communications path between your computer and the server when you dial in to a remote access server?

Session layer.

Explanation:

The main objective of the session layer they Sets up, maintains and ends contact sessions between the layer it is also responsible for keep the contact route between your machine and your server open when you connect to a remote server.

Instead of that, the session layer is also responsible for starting, shutting and maintaining the session between the application processes for the end-users.

So Session layer is the correct answer.