It happens to me quite often as well. If the problem is the Internet (which happens to all of us), then I stop the session early and ask the student to reshedule for another day.

The first few minutes of a call usually indicate how good or bad the Internet is going to be. And I'm always conscious that it could happen to me as well, so taking a hard line against students is counter-productive.  I'd rather just speak to the student another day when we can both focus on the class instead of the interruptions caused by a bad Skype connection.

If it is very bad and you cannot hear each other you should report a problem and reschedule because it is not the student's fault or yours. It is not fair for a student to pay if he/she cannot learn.

My policy is to ask the student to reschedule the lesson at a later date. I don't charge for this extra lesson. 

I've only had one bad experience due to internet problems. My student's internet connect was terrible. I asked to reschedule but he didn't want to do it l. The second lesson also had problems. So, I finally had to tell him to improve his connect if he wanted more lessons. I simply couldn't hear him. 

@Andi Thanks for the advice. You have WAY more experience than me, and I guess if it'll continue to happen in the future, I just gotta deal with it. The bad part is losing the current hour (plus Instant Tutoring) and the hour in the future, but in the long run that might lead to a good relationship with the student.

@aegis That's unfortunate. As a teacher I wouldn't teach if I couldn't guarantee on my end the internet was clear.

@Ruthi Similar to what I said to aegis, I wouldn't sign up for a session if I didn't think my internet would be good enough for it; I'd be courteous to the teacher. But Suzana above just told me a good option I didn't know about.