Insofar as avast! controls the servers and the streaming updates, no user control or direct input is available for this issue.
Streaming updates are for definition updates that cannot wait for the two or three daily main updates and/or are fixes applied for definition update errors or a tweaking in the main update made just prior. Different parts of the world have these streaming updates applied at differing times as threats arise, so what one might see in USA, these updates might not show up until a couple hours later elsewhere. Reason is due to deployment timing and any issues with the avast! server network that comes up.
So, for the above reasons, streaming update connectivity will come and go. Not much one can do about it.
In the worst case scenario, there is that emergency update feature, so if that works as it should, your expected protection should be always be available.
As long as one has the latest definitions, avast! can provide the protection needed, and coupled with safe surfing practices, one should be safe out there.