That year in your code is part of a copyright notice. It indicates the effective creation date of your software, which affects the time window of your copyright. It is not, strictly speaking, related to the license (although the MIT license happens to include a provision that the copyright notice must be preserved in all copies of the software).
You should update the year if and only if you made changes to your software in that year. Updating your copyright notice to include a year in which you made no copyrightable changes would be a misrepresentation of your copyright term. In the United States, this is currently only relevant if you are a corporation, but may be relevant to non-corporate authors in other countries. (In the U.S., copyright terms for natural individuals are currently a function of how long you live, not when you create a work.)
The FSF has some helpful guidance on including a correctly-dated copyright notice in your software (intended for use with the GPL, but applicable to all software):
The copyright notice should include the year in which you finished preparing the release (so if you finished it in 1998 but didn't post it until 1999, use 1998). You should add the proper year for each release; for example, “Copyright 1998, 1999 Terry Jones” if some versions were finished in 1998 and some were finished in 1999. If several people helped write the code, use all their names.
For software with several releases over multiple years, it's okay to use a range (“2008-2010”) instead of listing individual years (“2008, 2009, 2010”) if and only if every year in the range, inclusive, really is a “copyrightable” year that would be listed individually; and you make an explicit statement in your documentation about this usage.
It is not clear from the FSF guidance whether uploading incomplete, in-progress work to a public repository counts as "finishing a release". My guess is yes, if the work was deliberately made available for public download, but I'm not a lawyer.
So, to summarize:
if you made changes that year, do include the year in a comma-separated list in your copyright notice.
if did not make copyrightable changes that year, do not include that year in your copyright notice.