OP is not asking about booting to Single User mode, but how to restrict the access of a single user (i.e. one of many).
This may be available in a given distribution, but it isn't something that is directly supported at the operating system level of Linux, as such - so if it's not there already, it's going to be a job of actually writing something, I think.
You don't name the distribution you are running, nor whether this is a command-line login, or a login to a graphical desktop, or whatever... Comandline login process is handled by a program called 'tty' or 'getty' (stands for 'get teletype', from the dim and distant past of computing, for what it's worth). You may want to consider putting something in that intercepts the login process after getty has dealt with basic user-authentication - something that logs the user back out again, if they fail the additional criteria you have set for them, for instance.
Either way, its an additional layer of user management as far as I can see. For one thing, this is going to need some form of database, to keep count of number of logins per day and number of fluffed logins, et cetera.