I usually keep mine for awhile unless I find a sudden burst of inspiration to make something better. With the exception of this one I have now. Once the fair is over I'll swap to another one.
Avatar... a couple times a year. I last changed it in March. Before Judy Hopps it had been Reese for 5-6 months. Before that Rosie for a month. Before that Inkling Girl for six months. Then I think Toadette for like eight months before that haha.
Signature. My current signature is my PSN gamertag, and it's been that since New Years Eve I think. No intentions of changing it: I like that it automatically updates to share what game I've been playing lately. Before it was this I hadn't changed it in a year. I only did so because my previous one was about to become outdated haha.
I usually change my sig pretty often, like at least once a week. I usually change my avatar and cycle through a few that I use every few months. Sometimes I change it a lot though.
I try to find a set that I will stay with. That happens very easily on some forums, on others it doesn't happen easily at all.
Obviously when HHD finally brought two brass/woodwind instruments to the series, I had to feature that, because I would never shut up about it before. And I won't shut up if the next AC game doesn't have them, and doesn't have more. (with all of the different kinds of other instruments it's inexcusable).
My signature needs to be changed. The poor bassoon, I switched from it to oboe. Say what you will... If it weren't for the oboe, I would still be depressed working a lame overnight job like I was a year ago, feeling not alive. Instead, I quit that job and am back in school for music, going for what I want. Plus, I'm a much better musician than I ever was on the bassoon, and I'm having so much fun.
Okay, sorry, this topic isn't about that stuff... But I made a pretty dramatic signature here. I want to make an oboe one, but I just can't get back in the groove of making signatures. The last one I made was in 2012 or earlier.