Copyright protection law can be interpreted differently by legal systems in different countries. In the U.S., as indicated by the United States Copyright Office here, copyright protection begins:
The moment it is created and fixed in a tangible form that it is
perceptible either directly or with the aid of a machine or device.
Copyrights are only assignable however to original work. If you do not register your copyright with a copyright protection agency in your country (or international countries), your copyright claim would then be considered to be based on common law.
To indicate either a common law or registered copyright, it's standard practice to state the year you first "created and fixed in a tangible form" (i.e., published) said work (e.g., website, web application, etc...) in the form of:
Copyright © 2013 company/author
If you add minor revisions to your works, then it's not necessary to update the copyright year as indicated here. If your updates contains substantial changes to the original works:
it is considered to be a separate work of authorship in its own
right. The notice for such a derivative work should contain the date
the new work was published. The notice need not contain the date or
dates of the prior version or versions; however, it is common practice
to include such dates in the copyright notice.
In this case, it's considered common practice to indicate a range of years:
Copyright © 2013 - 2015 company/author
Dynamically changing the copyright year to the current year would be indicating that the date for either a copyright registration or common law copyright notice was the current year. This could weaken a claim to a copyright, as it might be argued by another party with the same content that they created the original work due to a prior copyright notice.
In short: Copyright notices should remain static, and reflect updates accordingly. For questions about copyright law and protection, it's wise to consult with an attorney who specializes in Intellectual Property.