Apple has now stopped signing iOS 10.3.1 firmware version for all the iOS devices like iPhone, iPad and iPod Touch which means that users can no longer downgrade or restore their iOS 10.3.1 using iTunes. Apple has closed the sign in window of iOS 10.3.1 just after the release of iOS 10.3.3 beta 4 and iOS 11 public beta last week.
As Apple stops signing iOS 10.3.1 firmware version, you can’t downgrade or restore to iOS 10.3.1 on iPhone, iPad and iPod touch. Along with that you can’t now save .SHSH blobs for iOS 10.3.1 and will not be able to downgrade from iOS 10.3.2. So whenever you try restoring your device to lower version you are basically forced to upgrade to iOS 10.3.2 directly.
If you have accidentally updated your device to iOS 10.3.2 via OTA or installed iOS 11 beta version, there is no longer possible to downgrade back nor restore to iOS 10.3.1 until you had a SHSH blobs saved for that.
Apple always gives two versions of iOS to restore whenever it releases a new version. So that people have ability to downgrade their devices to the previous version if they are not satisfied with the new one. But after some time, it stops signing the previous version.
You can also visit this link https://ipsw.me to check the signing status of Apple firmware.
Note: If you are on lower iOS versions like 10.3.1 stay away from update because jailbreak is is not yet available on this version and jailbreak for iOS 10.3.1 is coming soon. Recently, KeenLab has demoed jailbreak for iOS 10.3.2 and iOS 11 beta, there is chance of iOS 10.3.1 jailbreak. So if you are a jailbreakers it’s better to stay on older version of iOS for now.