Windows 7 unidentified public network

Very difficult question to even make a good guess on;
Typically when you see something like "Unidentified Public Network" it's because your wireless adapter is not receiving accurate DHCP addressing information from the wireless router, for which there could be any number of reasons;
1. It doesn't have any left it its' address pool to hand out.
2. The signal strength is so poor that reliable communications is impossible.
3. Sometimes wireless routers just stop handing out addresses (responding to DHCP requests) and need to be rebooted (not reset).
4. You can be connected to the wireless router and still not have an internet connection depending on what is going on, on the WAN side of the wireless router or if the wireless router is having trouble forwarding DNS queries.
Do you have physical control of the router? Can you reboot/reload it?
When you have the issue and perform an ipconfig /release and /renew what happens? Do you get an error of any kind like "Unable to contact a DHCP server", or when the problem is present and you perform an ipconfig /all what exactly is the ip addressing scheme that is present at that time, is anything missing, specifically a default gateway address? Do you have the most current driver for your network adapter from the network adapter manufacturer's website. Does the router have the most recent firmware update?
Since the problem seems intermitent there may be some outside interference to consider from other wireless devices, phones, radios, other wireless networks, etc.