We've been running the current version of the Strava app with iOS 7 (and above) and it's been working without any problems.
However, there is one setting that could cause a problem where the app loses GPS connection and stops recording any data. The setting is called "Background App Refresh" and this setting should be turned ON by default for all apps. It is required for Strava to continue to collect GPS data while in the background. If you don't have this setting enabled, you may see an error message pop-up when trying to record with the Strava app.
To Enable Background App Refresh:
Please go into your phone Settings > General > Background App Refresh and turn it to ON.
(Be sure to go to "General" as this is different than going to Settings > Strava > Background App Refresh