Q: Screen sharing revived by cycling WiFi off and on

I manage two laptops in my family that have this issue. Both are on El Capitan 10.11.3. Both frequently cannot be reached via Screen Sharing, which is turned on in the Sharing preference pane. Both have no problems using the internet in Safari or connecting to the mail server on the LAN. One of them, at least, cannot reach another computer on the LAN via Screen Sharing.

This is remedied by cycling WiFi off and on again on those two laptops.

It is really not a fix, as I sometimes need to be able to reach both, when neither have anyone who can do that off-on cycle on them. Does anyone have any idea, what might be going on?