For some reason, Tweetdeck does not have a server component, so it just runs in the background as a background process, making it potentially more likely to be suspended when memory gets tight. Running with a rooted Eris and memory set to stock functionality, I have no problems with Tweetdeck continuing to update in the background, but when I ran with the Autokiller app (which makes Android keep more RAM free) it was always getting suspended.

Unless you are running an automatic task killer, I'm not sure that there is much that you can do except contact Tweetdeck on their forum and ask if they would build a server component that would listen for notifications without being suspended (and, while they are at it, would be able to launch on phone restart.) I've asked for the feature myself, but I figure the more that people ask, the more likely it will happen.

 

Before trying a factory reset, do you have a lot of stored text messages or a lot of calls in your call log? I'm not sure that these take RAM (as opposed to storage), but I wonder if it does? There are apps that can delete messages older than a month, say, or keep your call log trimmed.

If that does not work, one of two other things (and I would usually not suggest this) is an automatic task killer, with Tweetdeck set as an exception.

If that still doesn't work - again, this is not something to do lightly, but you can consider rooting the phone. You can try running stock while rooted, giving you the ability to uninstall those apps that always run in the background that you may not be using (peep, footprints, amazon mp3 store - unless, of course, you are using them), or flash the ROM xtrSENSE, which runs just like stock 2.1 Eris, without these pesky problems. I just flashed xtrSENSE yesterday for the first time, though I've been rooted since May, and I installed about 58 third party apps, restored 175 sms messages, set up everything, and Tweetdeck is running just fine; I also have 42 MB RAM free.)

If you do think about rooting, you can learn a lot more in the "All things root" thread. Do note, though, that installing xtrSENSE will be just like doing a factory reset - the best thing is to start everything from scratch.

I hope that whatever you decide works.