Frequently when I generate a new password for a site, if the “Should Bitwarden save this password?” popup doesn’t show up (which happens disappointingly often) I’ll just lose the password forever. It would be nice if every generated password was saved automatically to my vault, per site. LastPass has this feature.
I see the “password history” feature, but this list isn’t saved/synced, and seems to get cleared on browser exit.
Open the browser extension, click the 
(“Generate”) button at the bottom, then scroll down to the bottom of the Generator screen, where you will see a Password history link. Click to see your previously generated passwords.
This history is specific for that browser extension on that device, and will not sync, but it is certainly retained on browser exit.
@grb Yes I mentioned this in the original post
You mentioned that the password history “isn’t saved”, and it “seems to get cleared on browser exit”, neither of which is true. You also said that when the prompt to save a password doesn’t come up, you " lose the password forever" — this is also not true, as you will be able to retrieve any generated password from the aforementioned Password History.
Since the feature you have requested already exists, I will close this thread. If you would like to request a feature that does not already exist, feel free to open a new Feature Request thread. However, if you’re new to Bitwarden and are unsure about whether or not a desired function exists (since it is possible that you don’t know where to find it), then you should post in the Ask the Community Forum instead.