Quail can kill themselves if repeatedly scared like that. It's causing preventable suffering ...... have you made it clear in a friendly but firm way to your neighbour the problems that the dog is causing to the quail. Some people just don't seem to get it. Someone told me that their dog was so friendly he would just 'play' with sheep
. Explained that it wasn't a good idea and why
. This was a holiday maker and the local farmers would have had more than a quiet word if his dog had gone to 'play' with the sheep. You may have to spell it out or invite them round to see the damage caused.
Terriers can be hard to contain. Father had a similar problem with a neighbours terrier and his chickens. Neighbour was elderly so dad reinforced the fence but explained that if the terrier continued to dig his way in despite wiring down then they would have to take measures to secure their garden.
If my dog was getting out I would consider it my duty to secure fencing and contain them.