Private snaps don’t get updated by snapd.
I see that snapd skips these snaps during its refresh stage:
232 Done 2017-10-19T13:47:49Z 2017-10-19T13:47:49Z Refresh all snaps: no updates
Even when there is a new revision in a particular private snap.
And by the way this is related to Why do devmode snaps not auto update?
Because “private” flag is generally used in conjunction with “devmode” flag when it’s not ready for public access, but developers want to take advantage of all the functionality of snapd, including automatic updates.
Devmode updates feature is marked as upcoming in the future. What about “private” updates? This would be great actually.