There are a couple of different reasons that your conversations may not be appearing. 

If your conversations disappeared after logging back into your account, it’s possible that you accidentally created a duplicate profile. Try logging out and logging back in with the method you originally used to create your account. If you did create a duplicate profile, all of your conversations will reappear as soon as you’re back in the correct account.

Your conversations could’ve also disappeared because you disabled Date mode. When Date mode is disabled, all of your matches and conversations are removed from your account. Unfortunately, conversations can’t be restored once Date mode has been disabled.  However, you’ll still be able to start fresh and make new matches if you enable Date mode again.