Safe Mode stuck often time appears on the jailbroken iPhone, iPad or iPod Touch, and very rare the same condition comes out on the non-jailbroken devices.
The reason this mode appears is because the app or tweak you have installed doesn't support the iOS version your phone is using, or because the tweak is corrupted to which effecting the Safe Mode condition. Or because of a crashed SpringBoard on iPhone, iPad or iPod Touch.
How to fix and avoid Safe Mode stuck on iPhone, iPad, iPod Touch
Step 1. If you install an app or tweak from Cydia, it's better for you to firstly read the description shown of the tweak, make sure it's supporting your device's OS version.
Step 2. It is recommended that you only install tweaks from a trusted repository or source like BigBoss, ModMyi, zodttd, etc. Because those repositories will not allow you to install a tweak that doesn't support your OS version.
Step 3. If you happen entering Safe Mode, then launch Cydia and uninstall any tweak or app that you installed recently before your iOS based devices entering Safe Mode.
Step 4. If the above step doesn't fix your problem, there is one thing you can do which is restarting your phone by pressing these buttons at the same time: Power and Home when the Apple logo appears then press and hold Volume UP for a few seconds. This trick to disable all the app or tweak's function that you previously installed from Cydia.
Step 5. The last effort. Let's say all the methods above failed, then use these: iLex Rat or semi restore, to deal with the problem.
Any questions? Then drop it on the comment area.