I have the same problem. I only ride once a week, too. What I do instead of trying to ride more often (cause I know my parents won't let me) is I try to get the most out of my lessons every time I go. After a lesson, I think about what I need to work on and set two goals for the next lesson (a flatwork goal and a jumping goal). Also, in between lessons, you can run or lift weights or do pilates to strengthen the muscles you use to ride. And don't forget to read lots about horses and watch tons of videos. =D
Every ride, good or bad, teaches you something new.