Stuck at Slide to unlock

I've owned a 3G, 4, 5 & 5S I've never had an issue at all with this ever, however last year i brought my mum a second hand iPhone 4 for christmas and its was fine until the ios7 update then she experienced the phone getting stuck on the slide to unlock screen, its not frozen as she can hold down the power button and turn it off and the phone unlocks fine after reboot, she was really sick of as it would happen about 3/4 times a day every day, we restored etc etc but problem persisted,

a few weeks ago it was her birthday and i thought i would buy her a new phone, she hated the 5C so i purchased myself the 5S and gave her my 5 (which i looked after very well) i didn't want the 5S to be honest, i don't like the grey colour instead of the darker black of the 5, anyways, thats a different story

she has had this phone about just under 2 weeks and its started doing it again!! same as before, its not frozen as she can hold down the power button and slide to turn off. why is she having this issue? i had the 5 for ages and I've never experienced this problem even on ios7 (I've had iOS 7 since beta) nor with my 5S, is she the problem? is she doing something?

any ideas?

That is peculiar. If it was just one iPhone, I'd blow it off as being a hardware issue, but yet another? Now I'm thinking there is something very buggy with her installation or an app she is using. She needs to start over with a clean install of iOS.

Make sure she has a complete backup of her iPhone:
iOS: How to back up and restore your content

Be sure to just do a backup, NOT a restore from backup.

Once done, use the "Restore iPhone" option:
https://support.apple.com/kb/ht1414

Once iOS is restored, you will then have the option to restore a backup. Do so then.

If she continues to have the problem, it may help to start keeping track of what app was last used before it locked up. That should be easy... just pull up the list of recently used apps (double-press Home button) and see what the app is on the far left of the list. If it consistently is a single app, then you likely have the culprit.

Agree with the above.

While apps should be running sandboxed - one person - same issue on two devices - and this issue being pretty rare - have to believe it is something they are running.

The issue is going to be since the phone won't open without powering off - you won't be able to double tap to see the last app used - she is going to have to either remember what was the last app she used before the issue reappears - or better have her keep a list and write them down every time she quits using the phone if need be to see if a single app reappears as the culprit.

A single device with this issue, would recommend trying a "reset" - not the same as a "restore".
To do a reset - press and hold the home and power buttons at the same time until it powers off and back on.