Profile date fields using YYYY-MM or MM YY don't work

If you create a custom field, and defined it as YYYY-MM format, and then add this custom field to a profile on a contribution page, once contribution is created, data is lost, and date reverts to today's year/month.

Reproduced in 4.7.12 and 4.7.16.

Steps to reproduce:
1) Create custom field. Define as date, format yyyy-mm
2) Add custom field to a profile
3) Add profile to a membership contribution page
4) Use it, and enter a month 5-6 years ago. (e.g., 2001-05)
5) Create an error (to force reload of form, e.g., leave credit card blank)
6) Go back to custom field.

Expected Results:
Date stays as 2001-05

Actual Results:
Date reverts to today's date.

Workaround
Don't use this feature! Use full date, or use year only.