There's a reasonable chance your Shareaza is firewalled and unable to obtain/sustain connections as a result.
Check some suggestions here: Shareaza FAQ - MOST COMMON PROBLEMS AND QUESTIONS and scroll down to how to open ports and port forwarding sections.

Also check https://portforward.com/router.htm

You can also check for any 3rd party security programs you might have installed to see if Shareaza is on their 'allowed' list for connecting to the internet.