I am suddenly having trouble sharing the screen of my work iMac from my MacbookPro at home and visa versa

Neither appear in the shared section of the Finder of the other. This is despite the fact that both are set up with my AppleID and have screen sharing turned on. To make the situation more interesting I have another computer on my home network, an older mac mini. The home Mac Mini does show up in the finder as shared both at work and on my MacbookPro at home. It is set up in the same way as the other two. I can screen share my mac mini from work or my work iMac from the home Mac mini. I can even share the mac mini from the work imac and then share the macbookpro from the screenshared mac mini! I can also screen share my work imac from the mac mini at home.

I have checked my settings on all 3 computers and they seem to be exactly the same.

The home MacbookPro has OS 10.9.2

The home Mac Mini has OS 10.7.5

The work iMac has 10.9.2

This has been very frustrating and puzzling. Any help would be much appreciated.

Thanks!