Does the papilla ever grow back in between your front teeth?

It is very dificult to surgically regenerate Papilla once it is gone. Almost impossible also it is rare/ not normal that papilla falls out while brushing ( one cause is pathology such as trench mouth /acute necrotizing gingivitis which causes punched out papilla , and is caused by stress / malnutrition) you will need to consult with a periodontist and have the site/ xray reviewed to diagnose underlying cause and look into treatments 

HelloIf you have natural teeth, papilla loss can be due to bone loss (periodontal disease)It is not possible to predictably get it back.There are possible treatment options from the restorative standpoint. A fine restorative dentist or prosthodontist can provide you with those solutions. If teeth have lost significant bone, the implants and prosthetic replacement may be another option.Dr. Kazemi

Unfortunately it is rare to have a papilla grow back but it is very case dependent.  I would suggest you contact a good periodontist to see if there is anything they suggest.  Good luck to you.