How much variance in my p-value

So l have a nuclear counting system which follows a poisson distribution. I have taken 5 data sets consisting of 30 counts each and l have used them in a chi squared gof test to see if they follow a poisson distribution. For each data set my p-value has been changing. Initially it was 0.5 then 0.7, 08, 02, 0.3 Is this normal or is it a cause of worry ?