Now I've set up a laptop dedicated to music production, how much do I actually need to stay connected to the Internet?  SONAR updates and such are always announced, so does it make sense to only go online when I need to for things like that, or do other things happen behind the scenes that I'd need to stay connected at any given moment?

Both my desktop and laptop have the wi-fi turned off until I have a reason to be online. I always make sure that the first thing I do after getting online is update my antivirus software, then I proceed with whatever the task is for the moment. As soon as I am done I turn off the wi-fi.
This works for me because I never have been much of an internet user anyway. Besides, I have a nice tablet for that sort of browsing.

I disable connectivity until I need something. Just no reason to leave a dedicated DAW connected IMO.

My DAW has always been online, all the time, rarely had a problem in 10 years.  Maybe I'm just lucky. I need to be able to send and receive files to and from collaborators, and back up files to Box.net and I like to do that quickly and  easily (yes, you'll get your tracks tomorrow Ed..)
 
YMMV.

You are going to get varied answers to this question.

My machine stays powered up and connected to the internet 24/7 via a Ethernet connection . Of course I have a firewall on the router itself and Malwarebytes on the PC. 
 
Microsoft release security patches ever second Tuesday of the month (Patch Tuesday). On the very rare occasion, Microsoft release security patches outside that cycle (out of band)

I just like to be able to, at the drop of a hat, check for any updates for any software that may be required without having to worry about reconnecting/disconnecting/reconnecting.  I just want the internet to be just their all the time.

I have never had an issue with Sonar Platinum with this configuration.

Thanks guys, just wanted to be sure before moving forward. It's actually kind of exciting to know I have an entire machine devoted just to making music. No conflicts with other software and apps, etc.  Not to mention I can leave the laptop in one place always hooked up and ready to go!

my DAW doubles as a Digital audio work station and a calculator
so I need to be online.
 
 

I'm with hockeyjx-  the only time my DAW is connected to the internet is when I need to download or update something.

All my DAWs and mixed systems have always been online all the time for the past fifteen years. I've never had it cause any problems. I too need the internet to send and receive files, mails, check for updates, look at tutorials or look up information. 

Sanderxpander
All my DAWs and mixed systems have always been online all the time for the past fifteen years. I've never had it cause any problems. I too need the internet to send and receive files, mails, check for updates, look at tutorials or look up information. 

same here, always online