I'm presuming all your members are stored in a database table somewhere.
1) If you want to restrict a user to a maximum number of times they can access ANY 'restricted' resource:-
Add two columns to the users table. 'last_accessed' column (default value of today's date) to store the date of last restricted page access and 'restricted_access_count' (default value of 0) to keep a count of restricted page accesses for the current day.
When a user accesses a restricted page, get the user's 'last_accessed' date and 'restricted_access_count' value.
If the date is before the current day, then user hasn't accessed any restricted content today, so update the 'last_accessed' date in the table, set 'restricted_access_count' to 1 and then give the user the requested page.
If the 'last_accessed' date is today, then check the 'restricted_access_count' value is not equal to or greater than your predefined limit. If it's below your limit, increment the 'restricted_access_count' and give them the page.
If the 'last_accessed' date is today and the 'restricted_access_count' is equal to or greater than your limit, don't give them the page.
2) If you want to set a user access limit for each resource, then you'll probably want to use general idea of above, but use an extra table to join your 'resource' table with your 'users' table and store access counts and dates in this join table.
This will work fine if you just want to limit access to PHP scripts. If you need to restrict access to other types of files (e.g. images), you'll need to use an intermediate PHP script to handle the access check and to then output the requested file.
Hope this helps. If you give us a better idea of your setup, may be able to provide some code examples.
Cheers,
Steven