Hi
You're right slicksps, there must be a reason if it is in the same place, like the place you turn to go somewhere more exciting, or is there a dog nearby or further up that she is anxious about? Has something happened there? A noise, or another dog woofed?
Also correct with the flexi, far too difficult to use the plastic handle effectively and actually dangerous by the side of a road if you accidently click the lock open

You can't use the lead either, as it is too thin to get any control on, so when you are walking use a normal lead and put the flexi in your pocket and change when you get to the park. It is also a good association for behaving on the short lead and can sniff and run on the long one.
If she stops, don't pull, she will only pull back at you as a counter action. instead, let the lead go loose, walk backwards to her side and then walk forward, positively, looking ahead - not at her, being very confident that she will come, use food if you can and walk smartly forward, as you start off forward again, give a small tug on your lead whilst movingn, but release immediately, (loose lead) as you do so. It is difficult to describe and I wish I could show it to you. You can also move to the side, or backwards and then forwards again, she should just start off after you.
Make sure as she is walking forward, you praise and give her a treat, in the position you want her, whilst she is moving forward, don't stop and treat her.
If she still doesn't follow you, then walk /run backwards calling her to you (as in a recall and then as she comes to you, move forward again, make sure you walk upright and positively, not giving her an opportunity to put her bum down again. Once more, treat her on the move, as you are walking.
It seems to be a phase that some dogs go through, a sort of avoidance techniue (sorry my letter to the left of W is not working!!!!!) and once they realise it doesn't work, they do give up. Just make sure that something really isn't scaring her, as forcing her past something she is fearful of, could make her worse.
Also, if you are walking at a good pace, it should be impossible for her to put her bum down, so get speed walking!!
Also, for a few days, don't treat the sit at all during lead work. Lots of people treat for the sit, but don't treat while the dog is walking forward! So naturally they sit at every opportunity.
Let us know how you get on.
Kate