Your post is confusing.
You ask if it is possible to log requests, and in the next sentence say that it works most of the time. What works most of the time, the logging or the request?
Are the failures always from the same machines, and if so what is different about these?
ITYM most but not all ssh logins do work.
I don't know your OS, so here is a general hint for Unix systems:
Ensure your sshd_config has SyslogFacility auth ,
then its standard log level is auth.info .
Enable this one in syslog.conf.
For even more info, you can change log level in syslog.conf to auth.debug .