Won't stay connected to network

Not sure if this is a Safari problem or internal with my Mac somehow. I have a G5 and I connect to a router for wireless internet. I also connect to my printer through the same router.

I've noticed sometimes when I exit safari and then come back to the computer later and click the Safari Icon it sometimes doesn't connect to the internet without me having to go through a "Network Diagnostic" test. Then usually what happens is about half way through the diagnostics my internet home page will load, or I'll get to the end of the diagnostic and it says "your connection is working" and then the home page will appear.

The problem I have now is that my computer won't stay connected to my printer. If I try to print a document or photo it does not send it to the printer, however if I turn Safari on so I know I'm connected to the network then all of a sudden the printer will work.

I guess somehow my computer is automatically disconnecting from my network and I'm not sure why or how to fix it. I've gone into the network preferences an it always shows "airport" is on and I always show all "solid" in the little icon at the top that looks like a "fan".

Any thoughts here on why my comp doesn't seem to stay connected to the network?

Thank you.