I presume you are referring to penalty points, when you refer in your question to 'points'.
Penalty points remain on your licence for 3 years from the start date (effective date). Any period in that time where your licence is out of date won’t count as part of the 3 years.
All penalty points added to a persons driving licence whether by way of payment of the fixed charge notice or by way of conviction in the courts are recorded by the Gardai and are also recorded on the national driver file.
This enables the Gardai to have access to all records regarding the number of penalty points on a person’s driving licence at any given time. Penalty points as you are probably aware, are not physically recorded on your licence.
I spoke to Driver Licensing division in Dept. Transport this afternoon and they have said you can enquire from them directly or at any Motor Tax office about your penalty points and when they will expire. I also think you receive a letter about 21 days before the points expire, notifying you they are being taken off your record.
Driver Licensing Division in Dept. Transport is contactable at Tel: (096) 78289 or LoCall: (1890) 406 040 Fax: (096) 24400. Contact information for your local motor tax office is available in your public telephone directory.