Uninstalling and reinstalling either program will "fix" the problem, but probably only until the next program update from avast. To work around this problem, in Sygate:
1. open Tools, then advanced rules.
2. In there, pick Add, enter whatever name you want the rule to have (such as avast).
3. click allow this traffic.
4. pick all interfaces (or the one you want)
5. Click hosts and click IP addresses.
6. Enter the following addresses:
195.70.130.34,66.98.166.72,216.127.72.135,216.12.202.5,66.98.196.85,67.15.0.83,67.15.0.90,217.31.49.244,195.47.75.50
7. click ports and protocols.
8. in protocol pick TCP.
9. in traffic direction pick outgoing.
You can pick a schedule or not. No application since that setup.avast changes all the time.
Sygate is doing what it should be doing by blocking an on the fly changed program from connecting to the outside world.
What this will do is to allow ALL outgoing traffic to connect to the avast servers and stop asking you over and over if it can connect.
OR, you can go into Tools, Options, Security and uncheck the anti-application hijacking option. However, if some virus/trojan/worm/whatever does what this option protects you from, you would not be protected. I decided that I didn't want this turned off, so used the above approach.
Either one of these works for me and several others I installed avast on their systems.