This is a question often asked by parents of kids with ADHD. Since the stimulants that have long been used to treat ADHD, like Ritalin, Concerta, and Adderall XR, could be given on an as needed basis, parents sometimes do stop them over the summer. Or they just give them on days they think their child will need them, such as during summer school, summer camps, or when they go on vacation.
Strattera is a little different than stimulants, since it takes a few weeks of taking it for it to work. So you really can't give it just on some days and not on others. You could still stop it over the summer, and then just remember to restart it 2-3 weeks before school starts again.
But should you stop your child's ADHD medicine? This is a silly question to some parents and Pediatricians. After all, a child with diabetes doesn't stop her insulin over the summer; kids who are farsighted don't stop wearing their glasses over the summer; and you still give your child with asthma his inhalers if he is wheezing during the summer. So why stop your child's ADHD medicines?
It can help to think about why your child with ADHD is even taking any medications. Is it just so that he will do better in school? Or is it to help his overall functioning and quality of life, which might include his school performance, but also includes his realtionships with his friends and family and how he functions at home and while playing. If your child's ADHD medicine, whether it is Strattera, Adderall XR, Concerta, etc., is helping his overall functioning, then you should likely give it to him everyday, even when he isn't in school.
You should also consider whether or not your child is having problems with his ADHD medication. Is it causing him to not gain weight well? Does it cause a lot of stomachaches and headaches? If your child is having side effects that can't be fixed by changing doses or changing medicines, then a break over the summer could be a good idea.