The only thing that expires is the written test. That is good for two years after you take it, and you can take it any time in your training as long as it's before the checkride.
It's probably actually less expensive to fly more often, because flying skills are perishable. If you fly once a month to make the monthly bill more palatable, you will spend the majority of your lessons relearning the feel of the airplane instead of learning new things, especially in the beginning. I was only able to fly once or twice on weekends for the majority of my flight training, and even a week-long gap sucked for me in the beginning. The weekends I got to fly Saturday and Sunday, the difference between my flying abilities on Saturday versus Sunday was pretty significant. As I got farther into training, the muscle memory took much longer to fade, and there were times I'd go a couple of weeks or nearly a month without flying and was able to just jump right back into where I'd left off.
Agreed. Initially I planned to fly at least once a week. I quickly realized that in order to meet that goal, I had to schedule at least twice a week so that at least one session would be a go. Toward the end of my basic training, I started scheduling three times a week, with the hope that two sessions would be a go.