I've got multiple OTP managers on my telephone. All of them seem to work with a constant timeout on the one-time passwords that are generated. For instance, the Microsoft authenticator works using a 6-digit time-based (T)OTP that is refreshing every 30 seconds.
The problem is that I often get an OTP that is valid for only a few seconds. The reason for that seems to be that the currently generated OTP is only left valid for that amount of seconds. While waiting some seconds for the next one isn't the end of the world, it does annoy me from a user-experience perspective. Often I find myself entering the code in the last few seconds, only for the code to timeout before I can hit enter.
Are there any OTP standards that somehow avoid this issue? If so, are there any authenticators that do always have a password ready for a reasonable amount of time, so that the number can always be copied before the timeout?
[EDIT] In hindsight the OTP is only shown for a couple of seconds, but the code may still be valid on the server some amount of time after that. However, this will leave the user very little time to copy the code - and that's probably the factor that takes most of the time.