For the first problem where the Windows 7 machines can't see each other
This is another Windows 7 bug apparently so you need to delate a rogue file to fix it.
The fix for this problem seems to be Deleting the file idstore.sst
Once everything at Peer Networking Grouping is running you may also need to do this... Start the Task Manager Click on the service Tab Find the "HomeGroupProvider" and then stop the service. You will need to restart after doing this.
For the dropped connection problem, that can be a million different things apparently, it can be anything from drivers
and router problelms to anti virus's or third party firewall's. I will start with the most common problem first.
Try using a different channel as RedBird suggested. If that doesn't change things read on. First make sure that your network adaptor is not set to turn off in your power options console.
Do you have anything from apple
installed on your system like quick time or itunes or Adobe software? If so it is possible for apples bonjour service to cause connection drop outs. If you have bonjour installed try this. Computer > Manage > Services and Applications > Services => find the bonjour service (sometimes is shown as long numbers), shutdown service, and set to Disabled.