Once you purchase RaceChrono Pro, you are allowed to re-install again for free, even when you buy a new phone or install it on your second device.
If Play Store asks you to purchase again, you’ll need to check a couple of things to have it sorted:
1) Check your purchases from Google Payments. To view your Play Store payment history, you must be logged in with same Google account as on your phone. Look for RaceChrono purchase.
2) Make sure you have the same Google Account activated on your phone, as the one that you made the purchase with.
3) If your purchase says Pro upgrade (RaceChrono), it means you have purchased the Pro upgrade in-app-purchase on the RaceChrono app. You will need to install RaceChrono, not RaceChrono Pro. The Pro upgrade is then automatically activated. RaceChrono with Pro upgrade is 100% similar to the RaceChrono Pro app. Only difference are the name and the icon.
4) If your purchase says RaceChrono Pro, it means you have purchased the separate RaceChrono Pro app, and you should be able to install it from Play Store without additional payments.
If you’re still having problems, do not hesitate to create a support request!