I know it is easier for many people to stop lessons over the summer- due to holidays, loss of the regular routine, limited time and so on, but in 16 years of teaching Piano I have first- hand seen what even a few weeks off can do to the progression of someone learning a musical instrument.
I came across this fantastic article and though to post what I thought was relevant here (source accredited at the bottom of the post):
“If you stop music lessons over the summer your child may experience:
1. Regression
Studies show that students who do not read during the summer tend to start behind their peers when school starts. The same holds true for playing an instrument. If students do not practice over the summer, any previous instruction can quickly be forgotten. Furthermore, once students do start their music lessons again, it can be frustrating to have to relearn lost material.
2. Loss of Interest
Taking a long break from learning something can lead to a loss of interest all together. Some families may start out thinking summer is just a time for a break, but all too often when there is a long lull in piano lessons, many students begin to lose interest in starting back up. What started out as a break turns into trying to motivate your kids again to like music at all.
3. Self discipline practice
With all the fun activities and free time that summer brings, a regular music lesson will help with your child’s self discipline. Quitting when something gets difficult or when something becomes less fun is not a great life lesson to teach. If you want your child to continue to develop skills of perseverance and self-discipline, sticking with something even when it’s supposed to be “summer break” will make them stronger.
4. The benefits of routine
Most parents have experienced what life is like with a routine and what happens in their homes when routine gets disrupted. Changes to regular meal times, sleep patterns or other daily routines can have a negative effect on a child’s behaviour. Regular music lessons can be considered part of a routine and provide structure and balance in the often busy and unstructured summer months.
Even though summer break is a time for relaxation and regrouping before the new school year, when it comes to piano lessons, children should continue with their regular schedule. Finding a balance where they can keep practicing without feeling stressed or overwhelmed while also not stopping completely is key.”
When I was learning Piano as a child, I took in more from my piano lessons in the summer as I didn’t have the distraction or stress given to me from school work.  It also gave me the time to realise that I really enjoyed learning music and felt like this was my time and my CHOICE to sit and learn the instrument in the relaxed setting of the summer holidays.  I also didn’t regress which ALL my students who pause their lessons do. It’s a waste of your money to pay for the same lesson you had three months ago for the first few lessons that you return back to lessons.
My overall advice: DON’T STOP your lessons and you will see the benefits!
Source: http://www.turnerskeyboards.com/stop-piano-lessons-summer/