Firstly, go to your Heroku dashboard, click on your Postgres addon, and in "durability" you can make a backup of the database. Then you can rest at ease that there is a backup.
Next, restart your dynos. That doesn't delete anything; it just reboots your app. That may fix the problem.
Next, look in your heroku logs (easiest way is to click on your Papertrail addon) and find what the cause for the crash is, then post that here.