I had the same issue
I had the same issue. My internet speeds would go down horrible from 8pm-1am every night. Down to 2-5 mb down/5-7 mb upload. I had this issue since after Hurricane Sandy. Finally last week they fixed the problem. After numerous calls, complains, & not giving up they finally took care of the matter. I was so angry with Verizon and I have no idea what causes those speeds to drop very low.
Fight for it! Call them. Also you can get response quickly through their FiOS Facebook Like Page. They are a lot better than calling technical support. Let me know how everything goes on your end!