If you look at there licenses, you will notice that the following text appears near the end of page.
"END OF TERMS AND CONDITIONS"
That is the end of the license. Nowhere above that text is there a requirement to add the year to the copyright notice. However, as pointed out in Stephen Kitt's answer, if you modify somebody else's program GPLv3 section 5 requires you to include a prominent notices stating that you modified it, with a date.
This requirement to record the date for changes you make to somebody else's program is to make sure that downstream recipients is made aware of modifications of the chronology and history of changes made to the original source code.
By law, your copyright is valid without a copyright notice (at least in Berne signatories, including the USA) - but if you leave it out (the notice, not the year), you may need to assert your copyright by other means if your copyright is challenged.
Going back to the web pages with the A(GPL) licenses, notice that below the "END OF TERMS AND CONDITIONS", there is a new headline:
How to Apply These Terms to Your New Programs
This is a helpful guideline - not a license requirement. Your license, and your copyright, is valid even if you choose to not follow this guideline.
However, it is a good idea to have a copyright notice with the year of publication. While not legally required, having such a notice in place may save you from proving that you've asserted your copyright by other means in the case of a dispute, and damages awarded may be reduced if there is no copyright notice in your work.