Making the most of Mentorships

What is the best way to not only connect with but engage meaningfully and long-term with mentors? I find that most of the time, we might meet once or sporadically. Another perspective, as a mentee, how can I create value for the mentor so that the relationship is worth it for them. I know there are a lot of platforms out there that might connect people together in this relationship, like: LinkedIn, alumni events, school platforms (i.e. handshake), but they don't seem to last very well.