We've been battling the license problems in my school district as well. The only fix I have to offer is manually inserting your license file to the computers having the problem. MOST of our machines do get the license file properly, but there are a good number that do not. It's a long process, but the only solution I have found.
On the machine claiming expired license/trial mode:
Open Avast
Click on the Maintenance Tab
Click 'Insert license file'
Locate and select your license file. (We have ours shared from our avast server and just UNC to the path)
It seems short and sweet, but when you have hundreds of machines that wont communicate with your central server it can get a bit tiresome.