It's even worst that that, if you remove the "start/end" date. But use display only YYYY-mm then the years is not saved. I'm moving this bug importance to critical (Data lost).

Apparently, I can't change the severity, neither edit my comment. Sorry.

It's always best with a clean and simple survey to reproduce the issue, and here better with a 2 page survey and allow previous.

The issue you're having is because of wrong dateformat used in a survey.
Year part should be entered with lowercase keys, like "yyyy".
So, if you enter date format like "yyyy-mm", survey would work correctly.
You can get an information about allowed date characters when you hover over "Date/Time format:" label on edit question page.

Also, there was a bug fix on Jun 14th which corrected date dropdown validation, so updating your installation to the latest version via ComfortUpdate could also help.

If you are still experiencing the same problem after following this tips, please upload .lss export file by selecting Display / Export --> Survey structure (.lss) in your survey.
Also, screenshots would be very helpful.

Version 3.12.3+180627 released