I use PS Touch on an Android tablet, and have reinstalled it without problems.
I would think you can do the same on an iPad.
As Jack said, I believe iTunes works similar to Google Play; any purchase you make under an iTunes or Google Play account will be honored should you have another device or get a new device so as long as you sign into that account.
(However, note that if you make a purchase under iTunes, you cannot retreive that purchase under Google Play and vice versa.)
It would be interesting to know which tutorial stopped working and if a restart of the application helps.
Btw please also provide information about what "stopped working" means.
Thank you all I reinstalled it and it works again, now I need to master this program