I think best solution would be fix the mentor system, where mentor/menteee dont have to be logged same time to get benefits.
If not I think there should be a queue of people who try to log some server. So everyone who try to log should be written how many people are before him to enter. Because writing pass for 1 h may be annoying. To make it better someone who can enter should have sound and after it that person should have 10 sec to press ok. If that person dont click ok he is kick from queue.