Cannot Share Screen with MBA which is behind Airport Extreme I'm trying to connect from iMac mid 2010 (10.8.3) to my MBA 2011 (10.8.3) using the Share Screen button in Finder.

I'm able to connect, but unfortunately the connection is closed in a minute and it's not possible to reconnect.

My MBA is behind Airport Extreme and my iMac is behind some 3rd party router.

Interesting that while I'm unable to connect to MBA, I can still mount the disk connected to the Airport.

How can I fix that?

EDIT

It appears that issue is only reproducible when clamshell of MBA is closed and system is asleep. That is, "Share Screen" works just fine if I ask someone to open clamshell and wake up the system. But if clamshell is closed, the issue I described above is always reproducible.

A little bit of info: I have File Vault enabled on MBA.
I am missing one critical detail in your description: How are you connecting?


VPN
iCloud / Back-to-my-Mac
LAN


Meanwhile - assuming it's either 1. or 2 - these are the quick check's I would perform initially and one-at-a-time. 


Check if it works the other way around: MBA -> iMac
If you connect via VPN, try Back-to-my-Mac instead
Make sure all routers run with current firmware
Both routers should have UPnP (non-Apple) and NAT-PMP (Apple) enabled. 
Some 3rd party routers allow more fine-tuning with UPnP. While this basically opens up your network (and makes it more insecure), I would go and open up for now, just to see if this solves the problem.
(temporarily) disable your firewall on both Macs. If you are running any 3rd party firewall app (such as LittleSnitch), switch if off for now.


Glad to hear if any of this opened your door again.