I don't know how many have had problems with the string stays that hold the top box in the open position........I certainly have.
The string ones that were on the bike wore out/broke and I tried various things to replace them, twine, electrical wire etc. none of which worked particularly well.
I found it hard to judge to the correct length on both sides and then tie off around the little bobbin thingies.
Then I tried cable ties (see picture). They have been brilliant, easy to install and what's more don't get caught between the two halves.
Get a largish cable tie, sit the lid about where you want it and mark the positions of the bobbins. Cut a lengthwise slit in the tie on the mark at each end and then trim the tie to an appropriate overall length.
Fit by pushing the tie where it is slit over the bobbins...you may have to lengthen the slit a little to get it over.
Voila...fixed
sD