First of all, I’ve checked my ASA which is an ASA5506 running version 9.8(2) and the enable command is something that is only available in global configuration mode (ASA(config#)). I’ve been able to change my enable password without problems. However, I did come across the following issue.
Take a look at the Cisco community post below. It indicates that there may be a bug on your particular ASA. Are you finding that the enable password is the same as the password of the user to log in to the device? If so you may have this command in your config:
aaa authentication sssh console LOCAL
Check your ASA version with the one in the post and see if it is the same problem.