Hiya Yasapple,
It sounds like you updated your phone and now when you set an alarm and tap save, it doesn't appear to stay in the Clock app. I would start by quitting the Clock app outright:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that force the device to restart the device with the Home and Sleep/Wake buttons as outlined in the following articleand test the issue again:
iOS: Turning off and on (restarting) and resetting
This should refresh the app and allow you to save your settings like you used to. I would also as a side note I would also recommend updating to iOS 9 if at all possible:
You can update software in iPhone Settings or by using iTunes.
Update wirelessly on iPhone. Go to Settings > General > Software Update. iPhone checks for available software updates.
Update software in iTunes. iTunes checks for available software updates each time you sync iPhone using iTunes. See Sync with iTunes.
For more information about updating iPhone software, see support.apple.com/HT204204.
From: Update iPhone
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