I am using plenty of 3rd party modules and have been for years.  This error crept up on me probably 6 months ago and has just gotten worse to the point where I need to do something.

It could also be my modules that I've made doing it.  I don't ever dispose of objects in my code or do any cleanup because I assume that will be taken care of by the framework.  Maybe that's my issue.

The memory error only occurs on my homepage.  If I get the error, then click to another page on the site, I don't see it.  If I go back to the homepage...there it is.  That would lead me to believe it's something on that page.  I've made modules only visible to admin on the page one by one to see if I still get the error...and I do.

I tend to think it's a cache issue because when I get the error..if I login as admin...it goes away.

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I'm too poor for anything other than the community version

That just means that sometime in that 3 minutes the asp.net process was restarted so you DNN instance had to do the JIT compile again and load everything back into memory.  You'd have to work with your hoster to figure out why the asp.net process was restarted.  If the time was longer between calls (15 minutes+) you applicaiton had to recompile / load back into memory becuase of time limits set by the hoster to keep sites alive.

I ran into somewhat like this earlier in the week.

In my case, and this took a fair bit of time to run down. I had installed the Events module, I got the newest one downloaded, uploaded and installed.

Then we found that it mostly worked installed on one portal, but when added to a second one, it would break on both.

So after research I found that the module was wrong version, removed it, got the older one up and ran fine for a few minutes then first portal started getting 'server not availble and other one just kept throwinfg connection re-set by peer every time.

Digging throw the logs, I found alot of errors on a couple events in the scheduler.  I disabled them both and site is backup